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A224143 Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A224143 #7 Aug 27 2018 16:53:46
%S A224143 16,86,275,691,1509,2985,5471,9431,15457,24285,36811,54107,77437,
%T A224143 108273,148311,199487,263993,344293,443139,563587,709013,883129,
%U A224143 1089999,1334055,1620113,1953389,2339515,2784555,3295021,3877889,4540615,5291151,6137961
%N A224143 Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A224143 Column 5 of A224146.
%H A224143 R. H. Hardin, <a href="/A224143/b224143.txt">Table of n, a(n) for n = 1..210</a>
%F A224143 Empirical: a(n) = (2/15)*n^5 + (2/3)*n^4 + (10/3)*n^3 + (25/3)*n^2 + (203/15)*n - 17 for n>2.
%F A224143 Conjectures from _Colin Barker_, Aug 27 2018: (Start)
%F A224143 G.f.: x*(16 - 10*x - x^2 + 11*x^3 + 8*x^4 - 10*x^5 + x^6 + x^7) / (1 - x)^6.
%F A224143 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.
%F A224143 (End)
%e A224143 Some solutions for n=3:
%e A224143 ..0..0..1..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..1
%e A224143 ..0..1..1..0..0....0..0..1..0..0....0..0..1..0..0....1..1..1..1..1
%e A224143 ..1..1..1..1..1....0..1..1..1..0....0..1..1..0..0....1..1..1..1..1
%Y A224143 Cf. A224146.
%K A224143 nonn
%O A224143 1,1
%A A224143 _R. H. Hardin_, Mar 31 2013