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A229479 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. 9
0, 1, 1, 2, 6, 2, 6, 42, 42, 6, 20, 248, 420, 248, 20, 70, 1312, 3328, 3328, 1312, 70, 246, 6528, 23964, 36116, 23964, 6528, 246, 854, 31232, 163528, 360912, 360912, 163528, 31232, 854, 2920, 145408, 1077588, 3443856, 5068384, 3443856, 1077588, 145408 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

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

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

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

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

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

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

.246..31232.1077588..31875248...900320160..24789931648...670127758336

.854.145408.6927888.288634368.11614790144.458660072320.17852292042240

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

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) = 8*a(n-1) - 16*a(n-2) for n > 4.

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

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

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

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

EXAMPLE

Some solutions for n=4, k=4:

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

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

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

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

CROSSREFS

Sequence in context: A229578 A078992 A062321 * A086356 A242435 A086359

Adjacent sequences:  A229476 A229477 A229478 * A229480 A229481 A229482

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Sep 24 2013

STATUS

approved

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Last modified August 4 17:55 EDT 2021. Contains 346455 sequences. (Running on oeis4.)