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A223764 Number of n X 2 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

%I A223764 #8 Feb 21 2018 11:57:38
%S A223764 4,12,28,56,101,169,267,403,586,826,1134,1522,2003,2591,3301,4149,
%T A223764 5152,6328,7696,9276,11089,13157,15503,18151,21126,24454,28162,32278,
%U A223764 36831,41851,47369,53417,60028,67236,75076,83584,92797,102753,113491,125051
%N A223764 Number of n X 2 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.
%C A223764 Column 2 of A223770.
%H A223764 R. H. Hardin, <a href="/A223764/b223764.txt">Table of n, a(n) for n = 1..210</a>
%F A223764 Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (5/4)*n + 1.
%F A223764 Conjectures from _Colin Barker_, Feb 21 2018: (Start)
%F A223764 G.f.: x*(2 - 2*x + x^2)^2 / (1 - x)^5.
%F A223764 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A223764 (End)
%e A223764 Some solutions for n=3:
%e A223764 ..0..0....0..0....0..0....1..0....1..1....0..0....0..1....0..1....0..0....0..1
%e A223764 ..0..0....0..0....1..1....0..1....0..1....1..0....1..1....0..0....1..0....0..1
%e A223764 ..1..1....0..1....1..1....0..0....0..1....0..1....0..1....0..0....1..1....1..0
%Y A223764 Cf. A223770.
%K A223764 nonn
%O A223764 1,1
%A A223764 _R. H. Hardin_, Mar 27 2013