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A229586 T(n,k)=Number of defective 3-colorings of an nXk 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order 14
0, 1, 0, 2, 6, 0, 6, 28, 40, 0, 16, 116, 264, 224, 0, 40, 444, 1620, 2160, 1152, 0, 96, 1620, 9156, 19764, 16416, 5632, 0, 224, 5724, 49848, 167364, 224532, 119232, 26624, 0, 512, 19764, 264300, 1375152, 2865780, 2440692, 839808, 122880, 0, 1152, 67068, 1374048 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

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

.0......6......28.......116.........444.........1620...........5724

.0.....40.....264......1620........9156........49848.........264300

.0....224....2160.....19764......167364......1375152.......11035044

.0...1152...16416....224532.....2865780.....35690460......435326724

.0...5632..119232...2440692....47091780....890824020....16551428868

.0..26624..839808..25745364...752194836..21639043284...613195191972

.0.122880.5785344.265720500.11768185764.515235810840.22285439501940

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..287

FORMULA

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) -16*a(n-2) for n>3

k=3: a(n) = 12*a(n-1) -36*a(n-2)

k=4: a(n) = 18*a(n-1) -81*a(n-2) for n>3

k=5: a(n) = 30*a(n-1) -261*a(n-2) +540*a(n-3) -324*a(n-4)

k=6: a(n) = 50*a(n-1) -805*a(n-2) +4662*a(n-3) -12150*a(n-4) +14580*a(n-5) -6561*a(n-6)

k=7: [order 8]

Empirical for row n:

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

n=2: a(n) = 6*a(n-1) -9*a(n-2) for n>4

n=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>6

n=4: [order 6] for n>12

n=5: [order 14] for n>18

n=6: [order 18] for n>26

n=7: [order 54] for n>60

EXAMPLE

Some solutions for n=3 k=4

..0..1..2..1....0..0..1..2....0..1..2..0....0..1..0..1....0..1..2..0

..0..1..2..0....1..2..0..2....0..2..1..2....0..2..0..0....0..0..2..0

..1..0..2..0....0..2..0..1....1..2..1..0....0..1..2..0....2..0..2..0

CROSSREFS

Row 1 is A057711(n-1)

Sequence in context: A327280 A241810 A156991 * A294789 A197035 A227805

Adjacent sequences:  A229583 A229584 A229585 * A229587 A229588 A229589

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Sep 26 2013

STATUS

approved

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Last modified January 21 16:22 EST 2020. Contains 331114 sequences. (Running on oeis4.)