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A303254 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303254 #6 May 11 2023 14:20:00
%S A303254 0,1,0,1,3,0,2,14,11,0,3,45,49,34,0,5,146,203,250,111,0,8,537,955,
%T A303254 1401,1183,361,0,13,1934,4556,10264,8664,5918,1172,0,21,6861,21843,
%U A303254 78679,106803,55624,28680,3809,0,34,24386,103319,584333,1218385,1105676,349273
%N A303254 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303254 Table starts
%C A303254 .0.....1......1........2..........3...........5.............8..............13
%C A303254 .0.....3.....14.......45........146.........537..........1934............6861
%C A303254 .0....11.....49......203........955........4556.........21843..........103319
%C A303254 .0....34....250.....1401......10264.......78679........584333.........4330427
%C A303254 .0...111...1183.....8664.....106803.....1218385......13529019.......153269484
%C A303254 .0...361...5918....55624....1105676....19457754.....322544617......5622650429
%C A303254 .0..1172..28680...349273...11394429...306224454....7600681910....204093228252
%C A303254 .0..3809.141255..2229806..118856245..4895684572..181926316054...7516309079483
%C A303254 .0.12377.691968.14141138.1230109648.77683246701.4319287740641.274539947294004
%H A303254 R. H. Hardin, <a href="/A303254/b303254.txt">Table of n, a(n) for n = 1..180</a>
%F A303254 Empirical for column k:
%F A303254 k=1: a(n) = a(n-1)
%F A303254 k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F A303254 k=3: [order 14]
%F A303254 k=4: [order 43] for n>44
%F A303254 Empirical for row n:
%F A303254 n=1: a(n) = a(n-1) +a(n-2)
%F A303254 n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
%F A303254 n=3: [order 19] for n>21
%F A303254 n=4: [order 63] for n>66
%e A303254 Some solutions for n=5, k=4
%e A303254 ..0..0..1..1. .0..1..0..0. .0..1..0..0. .0..0..1..1. .0..0..1..0
%e A303254 ..1..1..0..1. .1..0..0..0. .0..0..1..1. .0..1..0..0. .0..1..0..1
%e A303254 ..1..0..0..0. .1..0..1..0. .0..1..0..0. .1..0..0..1. .0..0..1..1
%e A303254 ..0..1..1..0. .0..1..1..1. .1..1..0..1. .1..1..1..1. .1..0..1..0
%e A303254 ..0..0..0..1. .0..0..0..1. .1..0..1..1. .0..0..0..0. .0..1..0..1
%Y A303254 Column 2 is A180762.
%Y A303254 Row 1 is A000045(n-1).
%Y A303254 Row 2 is A302225.
%Y A303254 Row 3 is A302473.
%Y A303254 Row 4 is A302474.
%K A303254 nonn,tabl
%O A303254 1,5
%A A303254 _R. H. Hardin_, Apr 20 2018