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A229534 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order. 13
0, 1, 0, 2, 4, 0, 6, 8, 20, 0, 16, 36, 58, 84, 0, 40, 112, 361, 356, 324, 0, 96, 368, 1588, 3064, 2038, 1188, 0, 224, 1152, 7460, 19276, 24344, 11184, 4212, 0, 512, 3568, 33136, 130854, 221096, 185808, 59626, 14580, 0, 1152, 10880, 146300, 833108, 2171944 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

.0.....1......2........6........16.........40...........96...........224

.0.....4......8.......36.......112........368.........1152..........3568

.0....20.....58......361......1588.......7460........33136........146300

.0....84....356.....3064.....19276.....130854.......833108.......5305746

.0...324...2038....24344....221096....2171944.....19965136.....184319130

.0..1188..11184...185808...2451728...34811238....463976296....6218438820

.0..4212..59626..1379512..26566266..544403948..10551803060..205336122417

.0.14580.311260.10036352.283010776.8359264560.236116939092.6668992563052

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..337

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1).

k=2: a(n) = 6*a(n-1) - 9*a(n-2) for n > 3.

k=3: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n > 5.

k=4: a(n) = 14*a(n-1) - 57*a(n-2) + 56*a(n-3) - 16*a(n-4) for n > 5.

k=5: [order 12] for n > 13.

k=6: [order 18] for n > 19.

k=7: [order 38] for n > 39.

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) - 8*a(n-3) - 4*a(n-4).

n=3: a(n) = 6*a(n-1) - a(n-2) - 28*a(n-3) - 4*a(n-4) + 16*a(n-5) - 4*a(n-6) for n > 8.

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

n=5: [order 20] for n > 22.

n=6: [order 46] for n > 48.

n=7: [order 92] for n > 94.

EXAMPLE

Some solutions for n=3, k=4:

  0 1 0 1     0 1 0 2     0 1 0 0     0 1 0 0     0 1 2 0

  0 2 0 2     1 2 0 2     0 1 2 1     2 1 2 1     0 1 2 0

  2 1 0 1     1 2 0 2     2 1 2 1     0 1 2 1     2 1 0 1

CROSSREFS

Column 2 is A167682(n-1).

Row 1 is A057711(n-1).

Sequence in context: A200165 A326938 A344031 * A021810 A073800 A076813

Adjacent sequences:  A229531 A229532 A229533 * A229535 A229536 A229537

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Sep 25 2013

STATUS

approved

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Last modified October 17 16:06 EDT 2021. Contains 348065 sequences. (Running on oeis4.)