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A223837 Number of n X 7 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223837 #10 Mar 18 2025 17:06:05
%S A223837 29,239,926,2578,6159,13582,28369,56607,108282,199047,352486,602938,
%T A223837 998945,1607388,2518375,3850945,5759652,8442093,12147444,17186068,
%U A223837 23940259,32876186,44557101,59657875,78980926,103473603,134247090,172596894,220024981,278263624,349301027
%N A223837 Number of n X 7 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223837 R. H. Hardin, <a href="/A223837/b223837.txt">Table of n, a(n) for n = 1..210</a>
%F A223837 Empirical: a(n) = (4/315)*n^7 - (1/45)*n^6 + (28/45)*n^5 + (113/72)*n^4 + (2137/180)*n^3 + (14023/360)*n^2 + (13159/140)*n - 339 for n>4.
%F A223837 Conjectures from _Colin Barker_, Aug 23 2018: (Start)
%F A223837 G.f.: x*(29 + 7*x - 174*x^2 + 238*x^3 + 109*x^4 - 256*x^5 + 45*x^6 + 111*x^7 - 27*x^8 - 26*x^9 + 6*x^10 + 2*x^11) / (1 - x)^8.
%F A223837 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>12.
%F A223837 (End)
%e A223837 Some solutions for n=3:
%e A223837 ..0..0..0..1..1..1..0....0..0..0..0..0..0..0....0..1..0..0..0..0..0
%e A223837 ..0..0..1..1..1..1..0....0..0..1..1..0..0..0....0..1..1..1..0..0..0
%e A223837 ..1..1..1..1..1..1..1....0..1..1..1..1..1..1....1..1..1..1..1..1..1
%Y A223837 Column 7 of A223838.
%K A223837 nonn
%O A223837 1,1
%A A223837 _R. H. Hardin_, Mar 27 2013
%E A223837 Name corrected by _Andrew Howroyd_, Mar 18 2025