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%I #6 Apr 19 2022 18:34:25
%S 1,2,2,3,3,3,5,6,6,5,8,11,9,11,8,13,22,25,25,22,13,21,46,60,85,60,46,
%T 21,34,91,160,261,261,160,91,34,55,182,396,838,1136,838,396,182,55,89,
%U 371,996,2644,5555,5555,2644,996,371,89,144,746,2480,8646,27902,39808,27902
%N T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ..1...2....3.....5......8.......13........21..........34...........55
%C ..2...3....6....11.....22.......46........91.........182..........371
%C ..3...6....9....25.....60......160.......396.........996.........2480
%C ..5..11...25....85....261......838......2644........8646........28076
%C ..8..22...60...261...1136.....5555.....27902......142396.......715457
%C .13..46..160...838...5555....39808....307759.....2396312.....18554951
%C .21..91..396..2644..27902...307759...3984553....50108120....631752599
%C .34.182..996..8646.142396..2396312..50108120..1000921717..20284433349
%C .55.371.2480.28076.715457.18554951.631752599.20284433349.666253766253
%H R. H. Hardin, <a href="/A326165/b326165.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +4*a(n-3) +a(n-5) -a(n-6)
%F k=3: [order 28] for n>30
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0
%e ..0..0..0..1. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
%e ..1..1..1..1. .0..0..0..0. .0..0..0..1. .1..1..0..0. .0..0..1..0
%e ..0..1..1..0. .0..0..0..0. .0..1..1..0. .0..1..1..1. .0..0..1..1
%e ..1..1..1..1. .1..0..0..0. .0..0..1..0. .0..0..1..1. .1..0..1..1
%Y Column 1 is A000045(n+1).
%Y Column 2 is A318031.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jun 09 2019
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