A229672 - OEIS

%I #9 Apr 28 2021 01:25:46

%S 0,0,0,1,4,1,3,61,61,3,12,652,1555,652,12,50,5048,19805,19805,5048,50,

%T 210,33152,194575,328160,194575,33152,210,861,197248,1673561,4331928,

%U 4331928,1673561,197248,861,3416,1098752,13271403,50919512,78681904

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

%H R. H. Hardin, <a href="/A229672/b229672.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 12*a(n-1) - 57*a(n-2) + 136*a(n-3) - 171*a(n-4) + 108*a(n-5) - 27*a(n-6) for n > 9.

%F k=2: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n > 6.

%F k=3: [order 6] for n > 7.

%F k=4: [order 12] for n > 14.

%F k=5: [order 27] for n > 29.

%F k=6: [order 63] for n > 65.

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

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

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

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

%e Table starts

%e ...0.......0........1..........3...........12.............50.............210

%e ...0.......4.......61........652.........5048..........33152..........197248

%e ...1......61.....1555......19805.......194575........1673561........13271403

%e ...3.....652....19805.....328160......4331928.......50919512.......557478448

%e ..12....5048...194575....4331928.....78681904.....1289285440.....19833096240

%e ..50...33152..1673561...50919512...1289285440....29775277216....649844491552

%e .210..197248.13271403..557478448..19833096240...649844491552..20240623720512

%e .861.1098752.99602405.5814322288.292113020848.13636997291008.608439629860544

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Sep 27 2013