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%I #7 Feb 27 2018 05:29:38
%S 1,42,3532,352184,36372976,3777546912,392658046912,40820345224064,
%T 4243729567634176,441184342397471232,45866192670977108992,
%U 4768319236090599225344,495721734753595527294976
%N Number of n X 6 matrices containing a permutation of 1..n*6 in increasing order rowwise, columnwise, diagonally and (downwards) antidiagonally.
%C Column 6 of A181196.
%H R. H. Hardin, <a href="/A181193/b181193.txt">Table of n, a(n) for n=1..100</a>
%F Empirical: a(n) = 120*a(n-1) - 1672*a(n-2) + 544*a(n-3) - 6672*a(n-4) + 256*a(n-5).
%F 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
%e Some solutions for 4 X 6:
%e ..1..2..3..4..5..6....1..2..3..4..5..6....1..2..3..4..5..6....1..2..3..4..5..6
%e ..7..8..9.10.11.12....7..8..9.10.11.12....7..8..9.10.11.12....7..8..9.10.11.12
%e .13.14.15.16.17.18...13.14.15.17.19.20...13.14.15.17.19.21...13.14.15.17.19.22
%e .19.20.21.22.23.24...16.18.21.22.23.24...16.18.20.22.23.24...16.18.20.21.23.24
%Y Cf. A181196.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 10 2010
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