editing

approved

R. H. Hardin, <a href="/A298454/b298454.txt">Table of n, a(n) for n = 1..180</a>

allocated for R. H. Hardin

T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 16, 0, 16, 0, 1, 48, 11, 11, 48, 1, 0, 88, 26, 161, 26, 88, 0, 1, 240, 46, 478, 478, 46, 240, 1, 0, 704, 204, 2459, 5938, 2459, 204, 704, 0, 1, 1600, 696, 15248, 22133, 22133, 15248, 696, 1600, 1, 0, 4032, 1493, 78163, 206239, 255029

1,5

Table starts

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

.1....4....4.....16.......48........88.........240...........704

.0....4....0.....11.......26........46.........204...........696

.1...16...11....161......478......2459.......15248.........78163

.0...48...26....478.....5938.....22133......206239.......2539477

.1...88...46...2459....22133....255029.....4095727......62979342

.0..240..204..15248...206239...4095727...112275165....2871621220

.1..704..696..78163..2539477..62979342..2871621220..141892377970

.0.1600.1493.390424.16116493.804773211.62756244756.4903035588074

Empirical for column k:

k=1: a(n) = a(n-2)

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

k=3: [order 17] for n>18

k=4: [order 53] for n>56

Some solutions for n=5 k=4

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

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

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

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

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

allocated

nonn,tabl

R. H. Hardin, Jan 19 2018

approved

editing

allocated for R. H. Hardin

allocated

approved