A181193 Number of n X 6 matrices containing a permutation of 1..n*6 in increasing order rowwise, columnwise, diagonally and (downwards) antidiagonally.

1, 42, 3532, 352184, 36372976, 3777546912, 392658046912, 40820345224064, 4243729567634176, 441184342397471232, 45866192670977108992, 4768319236090599225344, 495721734753595527294976

Offset

1,2

Comments

Column 6 of A181196.

Links

R. H. Hardin, Table of n, a(n) for n=1..100

Formula

Empirical: a(n) = 120*a(n-1) - 1672*a(n-2) + 544*a(n-3) - 6672*a(n-4) + 256*a(n-5).

Empirical g.f.: x*(1 - 78*x + 164*x^2 - 1976*x^3 + 224*x^4) / ((1 - 16*x)*(1 - 104*x + 4*x^2)*(1 + 4*x^2)). - Colin Barker, Feb 27 2018

Example

Some solutions for 4 X 6:
..1..2..3..4..5..6....1..2..3..4..5..6....1..2..3..4..5..6....1..2..3..4..5..6
..7..8..9.10.11.12....7..8..9.10.11.12....7..8..9.10.11.12....7..8..9.10.11.12
.13.14.15.16.17.18...13.14.15.17.19.20...13.14.15.17.19.21...13.14.15.17.19.22
.19.20.21.22.23.24...16.18.21.22.23.24...16.18.20.22.23.24...16.18.20.21.23.24

Crossrefs

Cf. A181196.

Sequence in context: A361370 A218409 A347169 * A227583 A347850 A053875

Adjacent sequences: A181190 A181191 A181192 * A181194 A181195 A181196

Keyword

nonn

Author

R. H. Hardin, Oct 10 2010

Status

approved