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A223839 Number of 3 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223839 #10 Mar 18 2025 18:08:11
%S A223839 4,16,48,118,255,503,926,1614,2690,4318,6712,10146,14965,21597,30566,
%T A223839 42506,58176,78476,104464,137374,178635,229891,293022,370166,463742,
%U A223839 576474,711416,871978,1061953,1285545,1547398,1852626,2206844,2616200,3087408,3627782,4245271
%N A223839 Number of 3 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223839 R. H. Hardin, <a href="/A223839/b223839.txt">Table of n, a(n) for n = 1..210</a>
%F A223839 Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (29/144)*n^4 + (11/48)*n^3 + (1007/360)*n^2 - (37/30)*n + 2.
%F A223839 Conjectures from _Colin Barker_, Aug 23 2018: (Start)
%F A223839 G.f.: x*(2 - 2*x + x^2)*(2 - 4*x + 5*x^2 - 4*x^3 + 2*x^4) / (1 - x)^7.
%F A223839 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A223839 (End)
%e A223839 Some solutions for n=3:
%e A223839 ..1..1..0....0..0..0....0..1..0....1..0..0....1..0..0....0..1..0....0..1..1
%e A223839 ..1..1..0....0..1..0....0..1..0....1..1..1....1..1..0....0..1..1....0..1..1
%e A223839 ..1..1..1....0..1..0....1..1..0....1..1..1....1..1..0....1..1..1....0..1..1
%Y A223839 Row 3 of A223838.
%K A223839 nonn
%O A223839 1,1
%A A223839 _R. H. Hardin_, Mar 27 2013
%E A223839 Name corrected by _Andrew Howroyd_, Mar 18 2025