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A223835 Number of n X 5 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223835 #10 Mar 18 2025 20:54:24
%S A223835 16,86,255,596,1240,2388,4325,7436,12222,19316,29499,43716,63092,
%T A223835 88948,122817,166460,221882,291348,377399,482868,610896,764948,948829,
%U A223835 1166700,1423094,1722932,2071539,2474660,2938476,3469620,4075193,4762780,5540466
%N A223835 Number of n X 5 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223835 R. H. Hardin, <a href="/A223835/b223835.txt">Table of n, a(n) for n = 1..210</a>
%F A223835 Empirical: a(n) = (2/15)*n^5 + (1/6)*n^4 + (19/6)*n^3 + (28/3)*n^2 + (126/5)*n - 36 for n>2.
%F A223835 Conjectures from _Colin Barker_, Aug 23 2018: (Start)
%F A223835 G.f.: x*(16 - 10*x - 21*x^2 + 36*x^3 + 9*x^4 - 18*x^5 + 2*x^6 + 2*x^7) / (1 - x)^6.
%F A223835 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 A223835 (End)
%e A223835 Some solutions for n=3:
%e A223835 ..1..0..0..0..0....1..1..1..0..0....1..0..0..0..0....0..1..1..0..0
%e A223835 ..1..1..1..1..0....1..1..1..0..0....1..1..1..1..0....1..1..1..1..1
%e A223835 ..1..1..1..1..1....1..1..1..1..0....1..1..1..1..0....1..1..1..1..1
%Y A223835 Column 5 of A223838.
%K A223835 nonn
%O A223835 1,1
%A A223835 _R. H. Hardin_, Mar 27 2013
%E A223835 Name corrected by _Andrew Howroyd_, Mar 18 2025