A229578 - OEIS

A229578

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

%I #8 Apr 27 2021 21:15:43

%S 0,1,1,2,6,2,6,26,26,6,20,80,76,80,20,70,216,171,171,216,70,246,544,

%T 362,312,362,544,246,854,1312,757,568,568,757,1312,854,2920,3072,1584,

%U 1064,924,1064,1584,3072,2920,9846,7040,3323,2064,1576,1576,2064,3323,7040

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

%C Table starts

%C ....0.....1.....2.....6....20....70...246...854..2920..9846..32810.108262

%C ....1.....6....26....80...216...544..1312..3072..7040.15872..35328..77824

%C ....2....26....76...171...362...757..1584..3323..6982.14673..30812..64615

%C ....6....80...171...312...568..1064..2064..4120..8384.17256..35728..74168

%C ...20...216...362...568...924..1576..2852..5440.10780.21880..45012..93232

%C ...70...544...757..1064..1576..2440..4048..7224.13696.27080..54928.112984

%C ..246..1312..1584..2064..2852..4048..6108..9992.17716.33504..66188.134200

%C ..854..3072..3323..4120..5440..7224..9992.14840.24072.42520..80296.158520

%C .2920..7040..6982..8384.10780.13696.17716.24072.35356.57008.100420.189400

%C .9846.15872.14673.17256.21880.27080.33504.42520.57008.83016.133216.234104

%H R. H. Hardin, <a href="/A229578/b229578.txt">Table of n, a(n) for n = 1..919</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) = 4*a(n-1) - 4*a(n-2) for n > 3.

%F k=3: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 5.

%F k=4: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 7.

%F k=5: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 7.

%F k=6: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 7.

%F k=7: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 7.

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

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

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

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

%Y Column 1 is A229472.

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Sep 26 2013