A229637 - OEIS

%I #8 Apr 27 2021 22:20:40

%S 0,0,0,1,6,0,3,40,39,0,12,122,244,202,0,40,488,1109,1496,925,0,120,

%T 1608,6031,10227,8800,3924,0,336,5392,28448,77620,89331,50084,15795,0,

%U 896,17368,136778,535671,960325,747299,277996,61182,0,2304,55232,633328

%N 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 Table starts

%C .0.....0.......1........3.........12..........40...........120............336

%C .0.....6......40......122........488........1608..........5392..........17368

%C .0....39.....244.....1109.......6031.......28448........136778.........633328

%C .0...202....1496....10227......77620......535671.......3723370.......25022190

%C .0...925....8800....89331.....960325.....9722206......98015235......960209886

%C .0..3924...50084...747299...11485716...170405645....2495874984....35693194243

%C .0.15795..277996..6049298..133784624..2902520386...61836040854..1290897457785

%C .0.61182.1513104.47723226.1525870912.48303362606.1498317588826.45634751291449

%H R. H. Hardin, <a href="/A229637/b229637.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n > 5

%F 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 k=4: [order 6] for n > 9.

%F k=5: [order 18] for n > 20.

%F k=6: [order 27] for n > 30.

%F k=7: [order 57] for n > 60.

%F Empirical for row n:

%F n=1: a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 6.

%F 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 n=3: [order 9] for n > 12.

%F n=4: [order 18] for n > 21.

%F n=5: [order 30] for n > 33.

%F n=6: [order 69] for n > 72.

%e Some solutions for n=3, k=4:

%e   0 1 0 2     0 1 0 1     0 1 0 2     0 1 0 0     0 1 1 2

%e   2 1 0 2     2 1 0 1     2 2 0 1     0 2 1 2     0 1 0 2

%e   2 1 2 0     1 2 0 1     1 1 0 1     0 2 1 0     0 1 0 1

%Y Column 2 is A229600.

%Y Row 1 is A052482(n-2).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Sep 27 2013