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R. H. Hardin, <a href="/A298133/b298133.txt">Table of n, a(n) for n = 1..197</a>

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T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 5, 4, 5, 0, 0, 10, 13, 13, 10, 0, 0, 25, 62, 15, 62, 25, 0, 0, 54, 223, 233, 233, 223, 54, 0, 0, 125, 826, 1055, 2621, 1055, 826, 125, 0, 0, 282, 3200, 5782, 21537, 21537, 5782, 3200, 282, 0, 0, 641, 12098, 36225, 175014, 285084, 175014

1,8

Table starts

.0...0.....0......0........0.........0...........0.............0..............0

.0...1.....2......5.......10........25..........54...........125............282

.0...2.....4.....13.......62.......223.........826..........3200..........12098

.0...5....13.....15......233......1055........5782.........36225.........205348

.0..10....62....233.....2621.....21537......175014.......1557284.......13225388

.0..25...223...1055....21537....285084.....3752401......52922003......714854991

.0..54...826...5782...175014...3752401....76791444....1706951987....36185741209

.0.125..3200..36225..1557284..52922003..1706951987...58599163176..1933759163417

.0.282.12098.205348.13225388.714854991.36185741209.1933759163417.99650656591710

Empirical for column k:

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

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

k=3: [order 18]

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

Some solutions for n=5 k=4

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

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

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

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

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

Column 2 is A297860.

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R. H. Hardin, Jan 13 2018

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