A229479 - OEIS

%I #7 Apr 27 2021 21:19:58

%S 0,1,1,2,6,2,6,42,42,6,20,248,420,248,20,70,1312,3328,3328,1312,70,

%T 246,6528,23964,36116,23964,6528,246,854,31232,163528,360912,360912,

%U 163528,31232,854,2920,145408,1077588,3443856,5068384,3443856,1077588,145408

%N T(n,k) = number of defective 4-colorings of an n X k 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.

%C Table starts

%C ...0......1.......2.........6..........20...........70............246

%C ...1......6......42.......248........1312.........6528..........31232

%C ...2.....42.....420......3328.......23964.......163528........1077588

%C ...6....248....3328.....36116......360912......3443856.......31875248

%C ..20...1312...23964....360912.....5068384.....68447552......900320160

%C ..70...6528..163528...3443856....68447552...1317269920....24789931648

%C .246..31232.1077588..31875248...900320160..24789931648...670127758336

%C .854.145408.6927888.288634368.11614790144.458660072320.17852292042240

%H R. H. Hardin, <a href="/A229479/b229479.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = 8*a(n-1) - 22*a(n-2) + 24*a(n-3) - 9*a(n-4) for n > 6.

%F k=2: a(n) = 8*a(n-1) - 16*a(n-2) for n > 4.

%F k=3: a(n) = 14*a(n-1) - 65*a(n-2) + 112*a(n-3) - 64*a(n-4) for n > 5.

%F k=4: [order 8] for n > 9.

%F k=5: [order 18] for n > 19.

%F k=6: [order 42] for n > 43.

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

%e   0 1 2 3     0 1 2 1     0 0 1 2     0 1 0 2     0 1 0 2

%e   2 3 1 1     2 3 0 2     1 3 0 1     3 0 1 3     2 3 1 0

%e   1 0 3 2     1 2 0 3     2 1 3 2     2 3 0 1     2 0 3 1

%e   3 2 0 1     3 1 2 1     0 2 1 3     0 2 3 2     1 2 0 3

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Sep 24 2013