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A302472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302472 #4 Apr 08 2018 10:16:32
%S A302472 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 A302472 1401,1147,361,0,13,1934,4556,10264,8493,5486,1172,0,21,6861,21843,
%U A302472 78679,101109,53575,25599,3809,0,34,24386,103319,584333,1141147,990266,331044
%N A302472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302472 Table starts
%C A302472 .0.....1......1........2.........3...........5.............8..............13
%C A302472 .0.....3.....14.......45.......146.........537..........1934............6861
%C A302472 .0....11.....49......203.......955........4556.........21843..........103319
%C A302472 .0....34....250.....1401.....10264.......78679........584333.........4330427
%C A302472 .0...111...1147.....8493....101109.....1141147......12546601.......139759054
%C A302472 .0...361...5486....53575....990266....16983273.....278275383......4682106140
%C A302472 .0..1172..25599...331044...9731423...251512646....6145486847....156721340433
%C A302472 .0..3809.121626..2075845..96648626..3770915891..137317050228...5300304476103
%C A302472 .0.12377.572657.12918219.950374395.55956081186.3037409718914.177368160967073
%H A302472 R. H. Hardin, <a href="/A302472/b302472.txt">Table of n, a(n) for n = 1..180</a>
%F A302472 Empirical for column k:
%F A302472 k=1: a(n) = a(n-1)
%F A302472 k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F A302472 k=3: [order 14]
%F A302472 k=4: [order 43] for n>44
%F A302472 Empirical for row n:
%F A302472 n=1: a(n) = a(n-1) +a(n-2)
%F A302472 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 A302472 n=3: [order 19] for n>21
%F A302472 n=4: [order 63] for n>66
%e A302472 Some solutions for n=5 k=4
%e A302472 ..0..1..0..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..1..1
%e A302472 ..0..0..1..1. .1..1..1..0. .0..0..1..1. .0..1..0..1. .1..0..0..0
%e A302472 ..1..1..1..1. .0..0..1..1. .1..1..0..1. .1..0..0..0. .1..1..1..1
%e A302472 ..1..0..1..0. .1..0..0..0. .1..0..0..0. .0..1..0..1. .0..0..0..1
%e A302472 ..0..0..0..1. .1..1..1..1. .1..1..1..0. .1..1..1..0. .1..1..1..0
%Y A302472 Column 2 is A180762.
%Y A302472 Row 1 is A000045(n-1).
%Y A302472 Row 2 is A302225.
%K A302472 nonn,tabl
%O A302472 1,5
%A A302472 _R. H. Hardin_, Apr 08 2018