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A223774 Number of n X 5 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

%I A223774 #7 Aug 23 2018 08:29:25
%S A223774 16,101,371,1040,2516,5573,11635,23230,44703,83305,150815,265901,
%T A223774 457485,769447,1267085,2045843,3242928,5052561,7745747,11695606,
%U A223774 17409482,25569241,37081383,53138828,75296493,105563057,146511615,201412251
%N A223774 Number of n X 5 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.
%C A223774 Column 5 of A223777.
%H A223774 R. H. Hardin, <a href="/A223774/b223774.txt">Table of n, a(n) for n = 1..210</a>
%F A223774 Empirical: a(n) = (1/3628800)*n^10 + (1/241920)*n^9 + (1/8640)*n^8 + (11/8064)*n^7 + (4273/172800)*n^6 + (589/11520)*n^5 + (649763/362880)*n^4 + (589/12096)*n^3 + (102443/2400)*n^2 - (16061/168)*n + 93 for n>2.
%F A223774 Conjectures from _Colin Barker_, Aug 23 2018: (Start)
%F A223774 G.f.: x*(16 - 75*x + 140*x^2 - 126*x^3 + 96*x^4 - 180*x^5 + 272*x^6 - 200*x^7 + 65*x^8 - 20*x^9 + 27*x^10 - 18*x^11 + 4*x^12) / (1 - x)^11.
%F A223774 a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>13.
%F A223774 (End)
%e A223774 Some solutions for n=3:
%e A223774 ..0..0..0..0..0....1..0..0..0..0....1..0..0..0..0....0..0..0..0..0
%e A223774 ..1..0..0..0..0....1..0..0..0..0....0..0..0..0..1....0..0..0..0..0
%e A223774 ..0..0..0..0..1....0..0..1..1..1....0..0..0..1..0....0..0..1..1..0
%Y A223774 Cf. A223777.
%K A223774 nonn
%O A223774 1,1
%A A223774 _R. H. Hardin_, Mar 27 2013