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A223840 Number of 4 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223840 #14 Mar 20 2025 14:53:31
%S A223840 5,25,89,249,596,1286,2578,4886,8851,15439,26072,42800,68523,107273,
%T A223840 164567,247843,366992,535000,768715,1089755,1525574,2110704,2888192,
%U A223840 3911252,5245153,6969365,9179986,11992474,15544709,20000411,25552941,32429513,40895846,51261286
%N A223840 Number of 4 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223840 R. H. Hardin, <a href="/A223840/b223840.txt">Table of n, a(n) for n = 1..210</a>
%F A223840 Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (19/2880)*n^6 + (7/180)*n^5 + (527/5760)*n^4 + (3683/1440)*n^3 + (4051/10080)*n^2 - (1707/280)*n + 13 for n>2.
%F A223840 Conjectures from _Colin Barker_, Aug 24 2018: (Start)
%F A223840 G.f.: x*(5 - 20*x + 44*x^2 - 72*x^3 + 89*x^4 - 70*x^5 + 28*x^6 - 4*x^7 + 4*x^8 - 4*x^9 + x^10) / (1 - x)^9.
%F A223840 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.
%F A223840 (End)
%e A223840 Some solutions for n=3:
%e A223840 ..0..0..0....0..1..0....0..0..0....0..1..0....0..0..0....0..0..0....0..0..0
%e A223840 ..0..0..0....0..1..0....0..0..0....0..1..1....0..0..0....0..0..1....0..0..0
%e A223840 ..0..0..0....0..1..0....1..0..0....1..1..1....0..0..0....0..0..1....0..1..0
%e A223840 ..0..0..1....1..1..1....1..1..0....1..1..1....0..1..1....0..1..1....0..1..0
%Y A223840 Row 4 of A223838.
%K A223840 nonn
%O A223840 1,1
%A A223840 _R. H. Hardin_, Mar 27 2013
%E A223840 Name corrected by _Andrew Howroyd_, Mar 20 2025