A181192 - OEIS

%I #8 Feb 27 2018 05:00:53

%S 1,14,290,6392,141696,3142704,69705920,1546100352,34293030016,

%T 760631058944,16871055411200,374205743270912,8300010573582336,

%U 184097055591849984,4083335265314938880,90569764059295875072

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

%C Column 5 of A181196.

%H R. H. Hardin, <a href="/A181192/b181192.txt">Table of n, a(n) for n=1..100</a>

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

%F Conjectures from _Colin Barker_, Feb 27 2018: (Start)

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

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

%F (End)

%e Some solutions for 4 X 5:

%e ..1..2..3..4..5....1..2..3..4..5....1..2..3..4..5....1..2..3..4..5

%e ..6..7..8..9.10....6..7..8..9.10....6..7..8..9.10....6..7..8..9.10

%e .11.12.13.14.15...11.12.13.14.17...11.12.13.14.16...11.12.13.14.18

%e .16.17.18.19.20...15.16.18.19.20...15.17.18.19.20...15.16.17.19.20

%Y Cf. A181196.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 10 2010