A229672 T(n,k) = number of defective 4-colorings of an n X k 0..3 array connected horizontally, antidiagonally and vertically with exactly two mistakes, and colors introduced in row-major 0..3 order.

0, 0, 0, 1, 4, 1, 3, 61, 61, 3, 12, 652, 1555, 652, 12, 50, 5048, 19805, 19805, 5048, 50, 210, 33152, 194575, 328160, 194575, 33152, 210, 861, 197248, 1673561, 4331928, 4331928, 1673561, 197248, 861, 3416, 1098752, 13271403, 50919512, 78681904

Offset

1,5

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 12*a(n-1) - 57*a(n-2) + 136*a(n-3) - 171*a(n-4) + 108*a(n-5) - 27*a(n-6) for n > 9.

k=2: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n > 6.

k=3: [order 6] for n > 7.

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

k=5: [order 27] for n > 29.

k=6: [order 63] for n > 65.

Example

Some solutions for n=3, k=4:
  0 1 0 1     0 1 2 3     0 1 2 0     0 1 0 2     0 1 2 0
  2 1 2 2     2 0 1 2     2 3 1 3     2 3 3 0     3 0 2 3
  3 0 1 3     3 3 1 3     0 1 3 0     1 2 0 2     1 0 1 0
Table starts
...0.......0........1..........3...........12.............50.............210
...0.......4.......61........652.........5048..........33152..........197248
...1......61.....1555......19805.......194575........1673561........13271403
...3.....652....19805.....328160......4331928.......50919512.......557478448
..12....5048...194575....4331928.....78681904.....1289285440.....19833096240
..50...33152..1673561...50919512...1289285440....29775277216....649844491552
.210..197248.13271403..557478448..19833096240...649844491552..20240623720512
.861.1098752.99602405.5814322288.292113020848.13636997291008.608439629860544

Crossrefs

Sequence in context: A085471 A064221 A378592 * A298568 A152890 A143354

Adjacent sequences: A229669 A229670 A229671 * A229673 A229674 A229675

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 27 2013

Status

approved