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Number of (n+2) X (n+2) 0..1 arrays with every 3 X 3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically.
+10
1
512, 8384, 124496, 1664470, 3515548, 11962178, 31663440, 59454484, 186710316, 670206564, 2390903880, 9098362320, 35531364902, 139249093536, 552399655264, 2200430718254, 8770350224230, 35026923585084, 140023496693106
EXAMPLE
Some solutions for n=3
..1..1..0..0..0....1..1..0..0..1....1..0..0..1..1....1..0..0..1..1
..0..1..0..1..1....0..0..0..0..1....1..0..0..0..1....1..0..0..0..0
..0..1..0..1..1....0..1..1..1..1....0..0..0..0..1....0..0..1..1..0
..0..1..1..1..0....0..0..1..1..0....0..1..1..1..1....1..0..0..1..1
..0..0..1..0..1....1..0..1..1..1....0..1..1..0..1....1..1..0..1..0
Number of (n+2)X(2+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically
+10
1
2440, 8384, 30184, 109666, 299727, 756553, 1786831, 3803056, 7637333, 14786984, 27386267, 48837015, 84729381, 143415507, 237363264, 385677751, 615912715, 969323806, 1506759547, 2315941896, 3521114537, 5307003996, 7939414563
FORMULA
Empirical: a(n) = 4*a(n-1) -5*a(n-2) +15*a(n-4) -44*a(n-5) +53*a(n-6) -8*a(n-7) -79*a(n-8) +196*a(n-9) -235*a(n-10) +88*a(n-11) +172*a(n-12) -472*a(n-13) +612*a(n-14) -392*a(n-15) -70*a(n-16) +656*a(n-17) -1054*a(n-18) +952*a(n-19) -426*a(n-20) -448*a(n-21) +1210*a(n-22) -1400*a(n-23) +1030*a(n-24) -112*a(n-25) -834*a(n-26) +1288*a(n-27) -1216*a(n-28) +584*a(n-29) +200*a(n-30) -728*a(n-31) +903*a(n-32) -628*a(n-33) +163*a(n-34) +232*a(n-35) -445*a(n-36) +364*a(n-37) -151*a(n-38) -32*a(n-39) +137*a(n-40) -116*a(n-41) +45*a(n-42) -20*a(n-44) +16*a(n-45) -4*a(n-46) for n>58
EXAMPLE
Some solutions for n=4
..0..1..1..1....0..0..0..0....0..0..1..0....0..0..0..0....0..0..1..0
..0..0..0..0....1..1..1..1....0..0..0..0....1..1..1..1....1..0..1..0
..0..1..1..1....0..0..0..0....0..1..0..1....0..0..0..1....0..0..1..1
..1..1..1..1....0..1..1..0....0..1..0..1....1..1..1..1....0..1..1..1
..0..0..1..0....0..1..1..1....1..1..0..1....1..1..1..1....0..0..0..1
..1..0..1..1....0..0..1..1....0..1..1..1....1..1..0..0....1..1..1..1
Number of (n+2)X(3+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically
+10
1
8392, 30184, 124496, 451721, 992616, 2326216, 4928792, 8796936, 15429736, 25901691, 41279336, 64590680, 98433380, 147871688, 219336822, 319580553, 459762302, 656093206, 925811194, 1292791666, 1788288642, 2455569322
FORMULA
Empirical: a(n) = 5*a(n-1) -12*a(n-2) +20*a(n-3) -20*a(n-4) -4*a(n-5) +54*a(n-6) -118*a(n-7) +161*a(n-8) -125*a(n-9) -8*a(n-10) +216*a(n-11) -425*a(n-12) +509*a(n-13) -398*a(n-14) +78*a(n-15) +370*a(n-16) -770*a(n-17) +972*a(n-18) -852*a(n-19) +417*a(n-20) +195*a(n-21) -804*a(n-22) +1188*a(n-23) -1230*a(n-24) +918*a(n-25) -336*a(n-26) -336*a(n-27) +918*a(n-28) -1230*a(n-29) +1188*a(n-30) -804*a(n-31) +195*a(n-32) +417*a(n-33) -852*a(n-34) +972*a(n-35) -770*a(n-36) +370*a(n-37) +78*a(n-38) -398*a(n-39) +509*a(n-40) -425*a(n-41) +216*a(n-42) -8*a(n-43) -125*a(n-44) +161*a(n-45) -118*a(n-46) +54*a(n-47) -4*a(n-48) -20*a(n-49) +20*a(n-50) -12*a(n-51) +5*a(n-52) -a(n-53) for n>83
Empirical polynomial of degree 13 plus a quasipolynomial of degree 8 with period 24 for n>30 (see link above)
EXAMPLE
Some solutions for n=3
..0..0..0..1..1....0..0..0..0..0....0..0..1..1..0....0..1..0..0..1
..0..0..0..0..1....0..0..0..1..0....0..0..0..1..1....0..0..0..0..1
..0..1..1..1..1....0..0..0..1..0....0..1..1..1..0....0..0..1..1..1
..0..1..1..1..0....0..0..0..1..1....1..1..1..1..1....1..0..0..0..0
..1..0..1..1..0....1..0..1..1..1....1..1..1..0..1....0..1..1..0..1
Number of (n+2)X(4+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically
+10
1
28540, 109666, 451721, 1664470, 3152822, 6795110, 13179071, 20815359, 34379873, 54238467, 84556277, 130915016, 198497618, 294992530, 439444601, 642097226, 927953195, 1323120836, 1881491639, 2642172439, 3680182112, 5073880259
FORMULA
Empirical: a(n) = 6*a(n-1) -17*a(n-2) +32*a(n-3) -40*a(n-4) +16*a(n-5) +58*a(n-6) -172*a(n-7) +279*a(n-8) -286*a(n-9) +117*a(n-10) +224*a(n-11) -641*a(n-12) +934*a(n-13) -907*a(n-14) +476*a(n-15) +292*a(n-16) -1140*a(n-17) +1742*a(n-18) -1824*a(n-19) +1269*a(n-20) -222*a(n-21) -999*a(n-22) +1992*a(n-23) -2418*a(n-24) +2148*a(n-25) -1254*a(n-26) +1254*a(n-28) -2148*a(n-29) +2418*a(n-30) -1992*a(n-31) +999*a(n-32) +222*a(n-33) -1269*a(n-34) +1824*a(n-35) -1742*a(n-36) +1140*a(n-37) -292*a(n-38) -476*a(n-39) +907*a(n-40) -934*a(n-41) +641*a(n-42) -224*a(n-43) -117*a(n-44) +286*a(n-45) -279*a(n-46) +172*a(n-47) -58*a(n-48) -16*a(n-49) +40*a(n-50) -32*a(n-51) +17*a(n-52) -6*a(n-53) +a(n-54) for n>90
Empirical polynomial of degree 14 plus a quasipolynomial of degree 8 with period 24 for n>36 (see link above)
EXAMPLE
Some solutions for n=2
..0..0..0..1..1..1....0..0..0..1..0..0....0..1..0..1..1..0....0..0..0..1..0..0
..0..1..0..0..1..1....1..0..0..1..1..1....1..1..0..1..1..1....1..0..0..1..0..0
..0..1..1..1..1..0....1..0..0..1..1..1....1..1..1..1..1..1....0..0..0..1..0..0
..1..0..1..1..1..1....1..1..1..1..0..0....0..0..1..0..1..1....0..0..0..1..0..1
Number of (n+2)X(5+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically
+10
1
91296, 299727, 992616, 3152822, 3515548, 6348659, 9470400, 11628396, 17673400, 27050795, 39953480, 60949836, 92326066, 139144143, 209469426, 313061550, 464262972, 684266432, 1000888422, 1452696403, 2091096410, 2987297421
FORMULA
Empirical: a(n) = 10*a(n-1) -47*a(n-2) +140*a(n-3) -298*a(n-4) +472*a(n-5) -532*a(n-6) +304*a(n-7) +320*a(n-8) -1264*a(n-9) +2226*a(n-10) -2756*a(n-11) +2441*a(n-12) -1110*a(n-13) -1041*a(n-14) +3456*a(n-15) -5366*a(n-16) +6044*a(n-17) -5090*a(n-18) +2616*a(n-19) +768*a(n-20) -4152*a(n-21) +6620*a(n-22) -7520*a(n-23) +6620*a(n-24) -4152*a(n-25) +768*a(n-26) +2616*a(n-27) -5090*a(n-28) +6044*a(n-29) -5366*a(n-30) +3456*a(n-31) -1041*a(n-32) -1110*a(n-33) +2441*a(n-34) -2756*a(n-35) +2226*a(n-36) -1264*a(n-37) +320*a(n-38) +304*a(n-39) -532*a(n-40) +472*a(n-41) -298*a(n-42) +140*a(n-43) -47*a(n-44) +10*a(n-45) -a(n-46) for n>71
Empirical polynomial of degree 15 plus a quasipolynomial of degree 5 with period 24 for n>25 (see link above)
EXAMPLE
Some solutions for n=1
..0..0..0..0..1..1..1....1..0..0..0..1..1..0....0..1..0..0..0..1..1
..0..1..1..1..1..1..1....0..0..0..0..0..0..1....1..0..0..1..1..1..0
..0..0..1..1..1..1..1....0..1..0..0..0..0..0....0..1..1..1..0..0..1
Number of (n+2)X(6+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically
+10
1
263476, 756553, 2326216, 6795110, 6348659, 11962178, 17762028, 22189517, 34970988, 55170420, 84715864, 133392623, 208289228, 322672996, 500237454, 770901679, 1177667175, 1786589429, 2690333088, 4017704901, 5947381463
FORMULA
Empirical: a(n) = 11*a(n-1) -57*a(n-2) +187*a(n-3) -438*a(n-4) +770*a(n-5) -1004*a(n-6) +836*a(n-7) +16*a(n-8) -1584*a(n-9) +3490*a(n-10) -4982*a(n-11) +5197*a(n-12) -3551*a(n-13) +69*a(n-14) +4497*a(n-15) -8822*a(n-16) +11410*a(n-17) -11134*a(n-18) +7706*a(n-19) -1848*a(n-20) -4920*a(n-21) +10772*a(n-22) -14140*a(n-23) +14140*a(n-24) -10772*a(n-25) +4920*a(n-26) +1848*a(n-27) -7706*a(n-28) +11134*a(n-29) -11410*a(n-30) +8822*a(n-31) -4497*a(n-32) -69*a(n-33) +3551*a(n-34) -5197*a(n-35) +4982*a(n-36) -3490*a(n-37) +1584*a(n-38) -16*a(n-39) -836*a(n-40) +1004*a(n-41) -770*a(n-42) +438*a(n-43) -187*a(n-44) +57*a(n-45) -11*a(n-46) +a(n-47) for n>77
Empirical polynomial of degree 17 plus a quasipolynomial of degree 7 with period 24 for n>33 (see link above)
EXAMPLE
Some solutions for n=1
..0..0..0..0..1..1..1..1....0..0..1..0..1..1..0..0....0..0..0..1..0..1..1..1
..0..1..1..0..1..1..1..0....0..0..0..0..0..1..1..0....0..0..0..0..0..1..1..1
..0..0..0..0..1..1..1..1....0..0..0..1..0..1..1..0....0..0..1..0..0..0..0..0
Number of (n+2)X(7+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically
+10
1
709704, 1786831, 4928792, 13179071, 9470400, 17762028, 31663440, 40874791, 67588814, 114752167, 187236938, 308804212, 504175746, 814016078, 1308165346, 2082298220, 3276474924, 5108994892, 7891481786, 12067402454, 18266075120
FORMULA
Empirical: a(n) = 10*a(n-1) -47*a(n-2) +140*a(n-3) -296*a(n-4) +452*a(n-5) -438*a(n-6) +24*a(n-7) +915*a(n-8) -2198*a(n-9) +3243*a(n-10) -3224*a(n-11) +1503*a(n-12) +1890*a(n-13) -6025*a(n-14) +9272*a(n-15) -9928*a(n-16) +7000*a(n-17) -782*a(n-18) -7052*a(n-19) +13941*a(n-20) -17350*a(n-21) +15759*a(n-22) -9296*a(n-23) -282*a(n-24) +10196*a(n-25) -17562*a(n-26) +20272*a(n-27) -17562*a(n-28) +10196*a(n-29) -282*a(n-30) -9296*a(n-31) +15759*a(n-32) -17350*a(n-33) +13941*a(n-34) -7052*a(n-35) -782*a(n-36) +7000*a(n-37) -9928*a(n-38) +9272*a(n-39) -6025*a(n-40) +1890*a(n-41) +1503*a(n-42) -3224*a(n-43) +3243*a(n-44) -2198*a(n-45) +915*a(n-46) +24*a(n-47) -438*a(n-48) +452*a(n-49) -296*a(n-50) +140*a(n-51) -47*a(n-52) +10*a(n-53) -a(n-54) for n>87
Empirical polynomial of degree 17 plus a quasipolynomial of degree 7 with period 24 for n>33 (see link above)
EXAMPLE
Some solutions for n=1
..0..0..0..0..0..0..1..1..1....0..0..0..0..1..0..1..0..1
..0..0..0..1..1..1..1..1..1....0..1..1..1..1..0..1..0..0
..1..0..0..1..0..1..1..1..1....1..1..0..0..0..1..1..0..1
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