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A223843 Number of 7 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223843 #7 Mar 18 2025 17:07:06
%S A223843 8,64,342,1356,4325,11749,28369,62869,130891,260219,499470,932402,
%T A223843 1701094,3042926,5348741,9253153,15773146,26518532,44008367,72142211,
%U A223843 116895662,187337832,297106834,466531024,725652569,1118500677,1709080380,2589696200,3892426882,5804817830
%N A223843 Number of 7 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223843 R. H. Hardin, <a href="/A223843/b223843.txt">Table of n, a(n) for n = 1..210</a>
%F A223843 Empirical: a(n) = (1/87178291200)*n^14 - (1/1779148800)*n^13 + (1/45619200)*n^12 - (53/136857600)*n^11 + (137/17418240)*n^10 - (1229/29030400)*n^9 + (739771/609638400)*n^8 - (1517923/87091200)*n^7 + (321517/691200)*n^6 - (12905723/3110400)*n^5 + (4378639787/119750400)*n^4 - (369357239/2494800)*n^3 + (61973609597/151351200)*n^2 - (519380551/360360)*n + 3759 for n>8.
%e A223843 Some solutions for n=3:
%e A223843 ..0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..0..1....1..0..0
%e A223843 ..0..0..0....1..0..0....0..0..0....0..0..0....0..1..0....0..0..1....1..0..0
%e A223843 ..0..1..0....1..1..0....1..0..0....0..0..0....0..1..0....0..0..1....1..1..0
%e A223843 ..0..1..0....1..1..0....1..1..0....0..0..0....0..1..1....0..0..1....1..1..0
%e A223843 ..0..1..0....1..1..0....1..1..0....1..1..0....1..1..1....0..1..1....1..1..0
%e A223843 ..0..1..0....1..1..0....1..1..0....1..1..0....1..1..1....0..1..1....1..1..1
%e A223843 ..0..1..0....1..1..0....1..1..1....1..1..0....1..1..1....0..1..1....1..1..1
%Y A223843 Row 7 of A223838.
%K A223843 nonn
%O A223843 1,1
%A A223843 _R. H. Hardin_, Mar 27 2013
%E A223843 Name corrected by _Andrew Howroyd_, Mar 18 2025