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A223834 Number of n X 4 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223834 #10 Mar 18 2025 17:07:42
%S A223834 11,46,118,249,471,824,1356,2123,3189,4626,6514,8941,12003,15804,
%T A223834 20456,26079,32801,40758,50094,60961,73519,87936,104388,123059,144141,
%U A223834 167834,194346,223893,256699,292996,333024,377031,425273,478014,535526,598089
%N A223834 Number of n X 4 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223834 R. H. Hardin, <a href="/A223834/b223834.txt">Table of n, a(n) for n = 1..210</a>
%F A223834 Empirical: a(n) = (1/3)*n^4 + (2/3)*n^3 + (31/6)*n^2 + (71/6)*n - 9 for n>1.
%F A223834 Conjectures from _Colin Barker_, Aug 23 2018: (Start)
%F A223834 G.f.: x*(11 - 9*x - 2*x^2 + 9*x^3 + x^4 - 2*x^5) / (1 - x)^5.
%F A223834 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
%F A223834 (End)
%e A223834 Some solutions for n=3:
%e A223834 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..0
%e A223834 ..0..0..0..0....0..0..0..0....0..1..0..0....1..1..1..0....1..1..1..0
%e A223834 ..0..1..1..0....0..1..1..1....0..1..1..0....1..1..1..0....1..1..1..0
%Y A223834 Column 4 of A223838.
%K A223834 nonn
%O A223834 1,1
%A A223834 _R. H. Hardin_, Mar 27 2013
%E A223834 Name corrected by _Andrew Howroyd_, Mar 18 2025