A229685 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
0, 0, 0, 0, 2, 0, 0, 36, 36, 0, 0, 360, 888, 360, 0, 0, 2688, 10896, 10896, 2688, 0, 0, 17280, 108000, 186576, 108000, 17280, 0, 0, 101376, 959040, 2700432, 2700432, 959040, 101376, 0, 0, 559104, 7952256, 35485776, 58038768, 35485776, 7952256, 559104, 0, 0
Offset: 1
Examples
Some solutions for n=3, k=4: 0 1 2 2 0 1 2 0 0 1 1 1 0 1 1 0 0 1 1 0 2 1 1 0 1 1 2 2 2 2 2 1 2 2 2 1 0 2 0 2 0 0 1 0 2 0 0 0 1 1 1 0 0 0 0 2 2 1 0 1 Table starts .0......0........0..........0............0..............0................0 .0......2.......36........360.........2688..........17280...........101376 .0.....36......888......10896.......108000.........959040..........7952256 .0....360....10896.....186576......2700432.......35485776........437924880 .0...2688...108000....2700432.....58038768.....1138164048......21063718224 .0..17280...959040...35485776...1138164048....33555543408.....937213830720 .0.101376..7952256..437924880..21063718224...937213830720...39647663129952 .0.559104.62892288.5169543120.373936700880.25175909234736.1617006498774912
Links
- R. H. Hardin, Table of n, a(n) for n = 1..220
Formula
Empirical for column k:
k=1: a(n) = a(n-1).
k=2: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n > 5.
k=3: a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3) for n > 4.
k=4: a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3) for n > 6.
k=5: [order 12] for n > 13.
k=6: [order 18] for n > 20.
k=7: [order 46] for n > 47.