A298454 -id:A298454

A298448

Number of nX2 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

+10
6

1, 4, 4, 16, 48, 88, 240, 704, 1600, 4032, 11072, 27392, 68608, 180736, 459776, 1160704, 2999296, 7682048, 19525632, 50081792, 128339968, 327434240, 837861376, 2145583104, 5483266048, 14023229440, 35888758784, 91776090112, 234707222528

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 2 of A298454.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)

EXAMPLE

Some solutions for n=7

..0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..1. .0..0. .0..0

..1..1. .1..1. .0..0. .0..0. .1..1. .1..1. .0..0. .1..0. .1..1. .0..0

..0..0. .1..1. .1..1. .1..0. .0..0. .1..1. .1..0. .1..1. .1..1. .1..1

..0..0. .0..0. .0..0. .1..0. .1..1. .1..1. .1..0. .1..0. .1..1. .1..1

..1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .0..1. .1..1. .0..0

..0..0. .0..0. .1..1. .1..0. .0..1. .1..1. .0..1. .0..0. .0..0. .0..0

..0..0. .1..1. .0..0. .0..1. .1..0. .1..1. .0..1. .0..0. .0..0. .0..0

CROSSREFS

Cf. A298454.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 19 2018

STATUS

approved

A298449

Number of nX3 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

+10
1

0, 4, 0, 11, 26, 46, 204, 696, 1493, 5880, 18994, 49941, 174020, 552946, 1590917, 5237693, 16486804, 49511202, 158599036, 497008665, 1523240497, 4815373712, 15059431049, 46604564297, 146391271270, 457401829113, 1422103399094

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 3 of A298454.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = a(n-1) +4*a(n-2) +21*a(n-3) -16*a(n-4) -60*a(n-5) -83*a(n-6) +55*a(n-7) +144*a(n-8) +125*a(n-9) +67*a(n-10) -98*a(n-11) -105*a(n-12) -92*a(n-13) +37*a(n-14) +11*a(n-15) -7*a(n-16) +3*a(n-17) for n>18

EXAMPLE

Some solutions for n=7

..0..1..1. .0..1..1. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .0..0..1

..1..1..1. .1..1..1. .1..0..1. .1..1..0. .1..1..1. .0..1..1. .1..0..0

..1..0..0. .1..0..0. .1..0..1. .0..0..0. .1..1..0. .0..1..1. .1..0..0

..1..0..0. .1..0..0. .1..1..1. .0..0..0. .1..1..0. .0..0..0. .0..0..0

..0..0..1. .1..1..1. .1..1..0. .1..0..1. .0..0..0. .0..1..1. .1..0..1

CROSSREFS

Cf. A298454.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 19 2018

STATUS

approved

A298450

Number of nX4 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

+10
1

1, 16, 11, 161, 478, 2459, 15248, 78163, 390424, 2230213, 11957077, 62686390, 343644381, 1857612208, 9915556165, 53695082023, 290087274436, 1558866184902, 8413068514505, 45404547945468, 244554296256136, 1318757750900979

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 4 of A298454.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 3*a(n-1) +9*a(n-2) +89*a(n-3) -204*a(n-4) -742*a(n-5) -2336*a(n-6) +5414*a(n-7) +16164*a(n-8) +22227*a(n-9) -51019*a(n-10) -155268*a(n-11) -9076*a(n-12) +216908*a(n-13) +348123*a(n-14) -565918*a(n-15) -423553*a(n-16) +2275697*a(n-17) +3018514*a(n-18) -4744310*a(n-19) -10714755*a(n-20) +1120597*a(n-21) +12707044*a(n-22) +14767028*a(n-23) -6781707*a(n-24) -13692035*a(n-25) -12330114*a(n-26) -4671661*a(n-27) +21721296*a(n-28) +14985223*a(n-29) +2432193*a(n-30) -25320474*a(n-31) -22704558*a(n-32) +17445078*a(n-33) +34393194*a(n-34) +3452869*a(n-35) -42645667*a(n-36) +551512*a(n-37) +18308956*a(n-38) -481318*a(n-39) -3378385*a(n-40) +2303479*a(n-41) +23871*a(n-42) -1901808*a(n-43) -170904*a(n-44) +588909*a(n-45) +106391*a(n-46) -40247*a(n-47) -13426*a(n-48) -10996*a(n-49) -462*a(n-50) +308*a(n-51) -40*a(n-52) +40*a(n-53) for n>56

EXAMPLE

Some solutions for n=7

..0..1..0..0. .0..1..0..0. .0..0..1..1. .0..1..1..0. .0..1..1..1

..1..0..0..0. .1..0..0..0. .1..1..1..1. .0..1..1..0. .0..1..1..1

..1..1..1..1. .0..0..1..1. .0..0..1..1. .1..1..1..1. .1..1..0..0

..1..1..0..0. .1..0..0..0. .0..0..0..0. .0..1..1..0. .0..1..1..1

..0..0..0..0. .1..0..1..1. .0..0..1..1. .1..0..0..1. .0..1..1..1

..1..1..0..1. .0..0..1..1. .1..0..1..1. .1..1..0..0. .0..0..1..0

..1..1..0..1. .0..0..0..0. .1..0..1..1. .1..1..0..0. .0..0..1..0

CROSSREFS

Cf. A298454.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 19 2018

STATUS

approved

A298451

Number of nX5 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

+10
1

0, 48, 26, 478, 5938, 22133, 206239, 2539477, 16116493, 140809027, 1454773733, 11442181688, 98650124977, 930856533076, 7893923708547, 68449197823238, 619698074500326, 5391736072793598, 47053275279174525, 418653067799229987

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 5 of A298454.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

EXAMPLE

Some solutions for n=6

..0..1..0..1..1. .0..0..0..0..0. .0..0..0..0..0. .0..1..1..0..0

..0..1..0..1..1. .0..0..1..0..0. .1..1..0..0..0. .0..1..1..0..0

..0..0..0..1..1. .1..1..1..1..0. .1..1..0..1..1. .0..0..0..1..1

..0..0..1..1..1. .1..1..1..0..0. .0..0..0..0..0. .0..0..0..1..1

..0..1..1..0..1. .1..0..0..0..0. .1..1..1..1..1. .1..0..1..1..1

..0..1..1..1..0. .0..1..0..1..1. .1..1..1..0..0. .0..1..1..0..0

CROSSREFS

Cf. A298454.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 19 2018

STATUS

approved

A298452

Number of nX6 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

+10
1

1, 88, 46, 2459, 22133, 255029, 4095727, 62979342, 804773211, 12648714013, 192361297807, 2716340306952, 40926079823971, 617074882316209, 9000146595771759, 134050098579479340, 2005238499337491454

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 6 of A298454.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

EXAMPLE

Some solutions for n=5

..0..0..1..1..1..0. .0..0..0..0..1..0. .0..1..1..0..1..0. .0..1..0..0..0..0

..1..1..1..1..1..0. .1..1..0..0..0..1. .0..1..1..0..1..0. .0..1..0..0..1..1

..1..1..0..0..1..1. .1..1..1..0..0..0. .0..0..0..0..1..1. .1..1..0..0..1..1

..1..1..0..0..1..1. .1..1..0..0..1..0. .0..0..1..0..0..1. .0..1..1..0..1..1

..1..1..0..0..1..1. .1..1..0..0..0..1. .0..0..1..0..0..1. .0..1..1..0..1..1

CROSSREFS

Cf. A298454.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 19 2018

STATUS

approved

A298453

Number of nX7 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

+10
1

0, 240, 204, 15248, 206239, 4095727, 112275165, 2871621220, 62756244756, 1680472622565, 43197208627165, 1038517293951991, 26665044675200600, 682574655104085964, 16923243467936517267, 429230559842341481820

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 7 of A298454.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

EXAMPLE

Some solutions for n=4

..0..0..1..1..1..1..1. .0..0..0..0..0..1..1. .0..0..0..0..0..0..0

..1..1..1..1..1..0..0. .0..0..0..0..0..0..0. .0..0..0..0..0..0..0

..1..1..0..0..1..1..1. .1..1..0..1..1..0..0. .0..1..1..1..1..0..1

..1..1..0..0..1..1..1. .1..1..0..1..1..1..1. .1..0..1..1..1..0..1

CROSSREFS

Cf. A298454.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 19 2018

STATUS

approved

A298447

Number of n X n 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

+10
0

0, 4, 0, 161, 5938, 255029, 112275165, 141892377970, 300456210546842

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Diagonal of A298454.

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

Some solutions for n=5

..0..0..1..1..0. .0..0..0..0..0. .0..1..1..0..1. .0..0..0..0..1

..1..1..1..0..1. .1..1..0..1..1. .1..0..1..1..0. .1..1..0..0..1

..0..0..1..1..1. .1..1..1..1..1. .1..1..1..0..0. .1..1..1..0..0

..0..0..1..1..0. .0..0..0..1..1. .1..0..1..1..0. .0..0..1..0..1

..1..1..1..0..1. .0..0..0..1..1. .0..1..1..0..1. .1..1..1..1..0

CROSSREFS

Cf. A298454.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 19 2018

STATUS

approved