A181192 Number of n X 5 matrices containing a permutation of 1..n*5 in increasing order rowwise, columnwise, diagonally and (downwards) antidiagonally.

1, 14, 290, 6392, 141696, 3142704, 69705920, 1546100352, 34293030016, 760631058944, 16871055411200, 374205743270912, 8300010573582336, 184097055591849984, 4083335265314938880, 90569764059295875072

Offset: 1

Author

R. H. Hardin, Oct 10 2010

Keywords

• nonn

Comments

Column 5 of A181196.

Examples

			Some solutions for 4 X 5:
..1..2..3..4..5....1..2..3..4..5....1..2..3..4..5....1..2..3..4..5
..6..7..8..9.10....6..7..8..9.10....6..7..8..9.10....6..7..8..9.10
.11.12.13.14.15...11.12.13.14.17...11.12.13.14.16...11.12.13.14.18
.16.17.18.19.20...15.16.18.19.20...15.17.18.19.20...15.16.17.19.20
		

Links

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

Crossrefs

Cf. A181196.

Formula

Empirical: a(n) = 24*a(n-1) - 40*a(n-2) - 8*a(n-3).

Conjectures from Colin Barker, Feb 27 2018: (Start)

G.f.: x*(1 - 10*x - 6*x^2) / ((1 - 2*x)*(1 - 22*x - 4*x^2)).

a(n) = 2^(n-2) + ((11-5*sqrt(5))^n*(2+sqrt(5)) + (-2+sqrt(5))*(11+5*sqrt(5))^n) / (4*sqrt(5)).

(End)