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A229637 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229637 #8 Apr 27 2021 22:20:40
%S A229637 0,0,0,1,6,0,3,40,39,0,12,122,244,202,0,40,488,1109,1496,925,0,120,
%T A229637 1608,6031,10227,8800,3924,0,336,5392,28448,77620,89331,50084,15795,0,
%U A229637 896,17368,136778,535671,960325,747299,277996,61182,0,2304,55232,633328
%N A229637 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%C A229637 Table starts
%C A229637 .0.....0.......1........3.........12..........40...........120............336
%C A229637 .0.....6......40......122........488........1608..........5392..........17368
%C A229637 .0....39.....244.....1109.......6031.......28448........136778.........633328
%C A229637 .0...202....1496....10227......77620......535671.......3723370.......25022190
%C A229637 .0...925....8800....89331.....960325.....9722206......98015235......960209886
%C A229637 .0..3924...50084...747299...11485716...170405645....2495874984....35693194243
%C A229637 .0.15795..277996..6049298..133784624..2902520386...61836040854..1290897457785
%C A229637 .0.61182.1513104.47723226.1525870912.48303362606.1498317588826.45634751291449
%H A229637 R. H. Hardin, <a href="/A229637/b229637.txt">Table of n, a(n) for n = 1..287</a>
%F A229637 Empirical for column k:
%F A229637 k=1: a(n) = a(n-1)
%F A229637 k=2: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n > 5
%F A229637 k=3: a(n) = 15*a(n-1) - 81*a(n-2) + 185*a(n-3) - 162*a(n-4) + 60*a(n-5) - 8*a(n-6) for n > 7.
%F A229637 k=4: [order 6] for n > 9.
%F A229637 k=5: [order 18] for n > 20.
%F A229637 k=6: [order 27] for n > 30.
%F A229637 k=7: [order 57] for n > 60.
%F A229637 Empirical for row n:
%F A229637 n=1: a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 6.
%F A229637 n=2: a(n) = 6*a(n-1) - 6*a(n-2) - 16*a(n-3) + 12*a(n-4) + 24*a(n-5) + 8*a(n-6).
%F A229637 n=3: [order 9] for n > 12.
%F A229637 n=4: [order 18] for n > 21.
%F A229637 n=5: [order 30] for n > 33.
%F A229637 n=6: [order 69] for n > 72.
%e A229637 Some solutions for n=3, k=4:
%e A229637   0 1 0 2     0 1 0 1     0 1 0 2     0 1 0 0     0 1 1 2
%e A229637   2 1 0 2     2 1 0 1     2 2 0 1     0 2 1 2     0 1 0 2
%e A229637   2 1 2 0     1 2 0 1     1 1 0 1     0 2 1 0     0 1 0 1
%Y A229637 Column 2 is A229600.
%Y A229637 Row 1 is A052482(n-2).
%K A229637 nonn,tabl
%O A229637 1,5
%A A229637 _R. H. Hardin_, Sep 27 2013