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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
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
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 A355007 A073800
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 25 2013
STATUS
approved