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A302224 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302224 #4 Apr 03 2018 12:16:35
%S A302224 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 A302224 675,361,0,13,1934,3425,6110,4237,2666,1172,0,21,6861,15569,38736,
%U A302224 40395,21777,9819,3809,0,34,24386,70323,251254,338204,292781,105585,37382
%N A302224 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302224 Table starts
%C A302224 .0.....1......1.......2.........3..........5...........8............13
%C A302224 .0.....3.....14......45.......146........537........1934..........6861
%C A302224 .0....11.....43.....164.......760.......3425.......15569.........70323
%C A302224 .0....34....194.....934......6110......38736......251254.......1610569
%C A302224 .0...111....675....4237.....40395.....338204.....3018243......26373655
%C A302224 .0...361...2666...21777....292781....3420704....42508145.....524715109
%C A302224 .0..1172...9819..105585...2043848...32181643...553097760....9458629708
%C A302224 .0..3809..37382..523414..14419536..310963650..7403262824..177191137344
%C A302224 .0.12377.140039.2578424.101511446.2973099477.97939043966.3265007473096
%H A302224 R. H. Hardin, <a href="/A302224/b302224.txt">Table of n, a(n) for n = 1..181</a>
%F A302224 Empirical for column k:
%F A302224 k=1: a(n) = a(n-1)
%F A302224 k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F A302224 k=3: [order 11]
%F A302224 k=4: [order 30] for n>34
%F A302224 k=5: [order 92] for n>97
%F A302224 Empirical for row n:
%F A302224 n=1: a(n) = a(n-1) +a(n-2)
%F A302224 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 A302224 n=3: [order 15] for n>17
%F A302224 n=4: [order 54] for n>58
%e A302224 Some solutions for n=5 k=4
%e A302224 ..0..0..1..1. .0..0..1..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
%e A302224 ..0..1..1..1. .1..1..0..1. .0..1..0..1. .1..1..1..0. .0..1..1..1
%e A302224 ..1..0..0..0. .1..1..0..0. .1..0..0..1. .0..0..0..0. .1..0..0..0
%e A302224 ..1..1..1..1. .1..0..0..1. .1..1..1..1. .0..1..1..1. .0..0..1..1
%e A302224 ..0..0..0..0. .1..1..1..0. .0..0..0..0. .0..0..1..1. .0..0..1..1
%Y A302224 Column 2 is A180762.
%Y A302224 Row 1 is A000045(n-1).
%K A302224 nonn,tabl
%O A302224 1,5
%A A302224 _R. H. Hardin_, Apr 03 2018