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A181194 Number of n X 7 matrices containing a permutation of 1..n*7 in increasing order rowwise, columnwise, diagonally and (downwards) antidiagonally.

%I A181194 #6 Feb 27 2018 05:32:39
%S A181194 1,132,49100,25097600,14083834704,8092149471168,4673805856338368,
%T A181194 2702482348019033600,1562998915785444034816,904016986809953084011520,
%U A181194 522876616523380188491377664,302428597238403007787949047808
%N A181194 Number of n X 7 matrices containing a permutation of 1..n*7 in increasing order rowwise, columnwise, diagonally and (downwards) antidiagonally.
%C A181194 Column 7 of A181196.
%H A181194 R. H. Hardin, <a href="/A181194/b181194.txt">Table of n, a(n) for n=1..100</a>
%F A181194 Empirical: a(n) = 720*a(n-1) - 84448*a(n-2) + 1503360*a(n-3) - 17912224*a(n-4) - 318223104*a(n-5) + 564996096*a(n-6) + 270471168*a(n-7) - 11373824*a(n-8) + 65536*a(n-9).
%F A181194 Empirical g.f.: x*(1 - 588*x + 38508*x^2 - 610624*x^3 - 20571792*x^4 + 98269760*x^5 + 112896832*x^6 - 6488576*x^7 + 57344*x^8) / ((1 - 2*x)*(1 - 26*x + 512*x^2)*(1 - 114*x - 1156*x^2 + 8*x^3)*(1 - 578*x - 228*x^2 + 8*x^3)). - _Colin Barker_, Feb 27 2018
%e A181194 Some solutions for 4 X 7:
%e A181194 ..1..2..3..4..5..6..7....1..2..3..4..5..7.10....1..2..3..4..5..7.10
%e A181194 ..8..9.10.11.12.13.14....6..8..9.12.13.15.19....6..8..9.12.13.15.19
%e A181194 .15.16.17.18.19.20.21...11.14.17.18.20.22.24...11.14.17.18.20.22.25
%e A181194 .22.23.24.25.26.27.28...16.21.23.25.26.27.28...16.21.23.24.26.27.28
%Y A181194 Cf. A181196.
%K A181194 nonn
%O A181194 1,2
%A A181194 _R. H. Hardin_, Oct 10 2010