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A302670 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302670 #4 Apr 11 2018 11:59:56
%S A302670 0,1,0,1,3,0,2,14,11,0,3,45,43,34,0,5,146,164,194,111,0,8,537,760,934,
%T A302670 691,361,0,13,1934,3425,6110,4267,2802,1172,0,21,6861,15569,38736,
%U A302670 42367,21949,10660,3809,0,34,24386,70323,251254,352174,316977,106793,41839
%N A302670 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302670 Table starts
%C A302670 .0.....1......1.......2.........3..........5............8............13
%C A302670 .0.....3.....14......45.......146........537.........1934..........6861
%C A302670 .0....11.....43.....164.......760.......3425........15569.........70323
%C A302670 .0....34....194.....934......6110......38736.......251254.......1610569
%C A302670 .0...111....691....4267.....42367.....352174......3204956......28324200
%C A302670 .0...361...2802...21949....316977....3640304.....46360666.....582115385
%C A302670 .0..1172..10660..106793...2320879...35549458....637088915...11181864782
%C A302670 .0..3809..41839..529984..17037458..353912413...8880747825..219692176894
%C A302670 .0.12377.161878.2617548.125456575.3503182605.123521424862.4291098950499
%H A302670 R. H. Hardin, <a href="/A302670/b302670.txt">Table of n, a(n) for n = 1..180</a>
%F A302670 Empirical for column k:
%F A302670 k=1: a(n) = a(n-1)
%F A302670 k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F A302670 k=3: [order 14]
%F A302670 k=4: [order 32] for n>35
%F A302670 Empirical for row n:
%F A302670 n=1: a(n) = a(n-1) +a(n-2)
%F A302670 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 A302670 n=3: [order 15] for n>17
%F A302670 n=4: [order 54] for n>58
%e A302670 Some solutions for n=5 k=4
%e A302670 ..0..0..1..1. .0..0..1..1. .0..1..1..0. .0..1..1..1. .0..1..1..0
%e A302670 ..1..1..0..1. .0..1..0..0. .1..0..0..1. .0..0..1..1. .1..0..0..1
%e A302670 ..1..1..0..1. .1..0..1..1. .1..1..0..0. .1..0..0..0. .1..0..0..1
%e A302670 ..0..0..1..0. .0..0..1..0. .0..1..0..1. .0..1..1..1. .1..1..1..1
%e A302670 ..0..0..1..1. .1..1..0..1. .1..0..1..1. .1..0..0..1. .0..0..0..0
%Y A302670 Column 2 is A180762.
%Y A302670 Row 1 is A000045(n-1).
%Y A302670 Row 2 is A302225.
%Y A302670 Row 3 is A302226.
%Y A302670 Row 4 is A302227.
%K A302670 nonn,tabl
%O A302670 1,5
%A A302670 _R. H. Hardin_, Apr 11 2018