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.

0, 1, 1, 2, 6, 2, 6, 26, 26, 6, 20, 80, 76, 80, 20, 70, 216, 171, 171, 216, 70, 246, 544, 362, 312, 362, 544, 246, 854, 1312, 757, 568, 568, 757, 1312, 854, 2920, 3072, 1584, 1064, 924, 1064, 1584, 3072, 2920, 9846, 7040, 3323, 2064, 1576, 1576, 2064, 3323, 7040

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OFFSET

1,4

COMMENTS

Table starts

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

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

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

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

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

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

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

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

.2920..7040..6982..8384.10780.13696.17716.24072.35356.57008.100420.189400

.9846.15872.14673.17256.21880.27080.33504.42520.57008.83016.133216.234104

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..919

FORMULA

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) - 4*a(n-2) for n > 3.

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

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

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

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

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

EXAMPLE

Some solutions for n=3, k=4:

0 1 2 3 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1

2 1 0 1 2 3 2 3 3 2 3 1 2 3 2 3 2 3 2 3

0 3 2 3 0 1 0 3 1 0 3 2 0 3 1 0 0 0 1 0

CROSSREFS

Column 1 is A229472.

Sequence in context: A241040 A151705 A170861 * A078992 A062321 A229479

Adjacent sequences: A229575 A229576 A229577 * A229579 A229580 A229581

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Sep 26 2013

STATUS

approved