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A223833 Number of n X 3 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223833 #10 Mar 18 2025 18:18:29
%S A223833 7,22,48,89,149,232,342,483,659,874,1132,1437,1793,2204,2674,3207,
%T A223833 3807,4478,5224,6049,6957,7952,9038,10219,11499,12882,14372,15973,
%U A223833 17689,19524,21482,23567,25783,28134,30624,33257,36037,38968,42054,45299,48707,52282
%N A223833 Number of n X 3 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223833 R. H. Hardin, <a href="/A223833/b223833.txt">Table of n, a(n) for n = 1..210</a>
%F A223833 Empirical: a(n) = (2/3)*n^3 + (3/2)*n^2 + (35/6)*n - 1.
%F A223833 Conjectures from _Colin Barker_, Aug 23 2018: (Start)
%F A223833 G.f.: x*(7 - 6*x + 2*x^2 + x^3) / (1 - x)^4.
%F A223833 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A223833 (End)
%e A223833 Some solutions for n=3:
%e A223833 ..0..1..0....1..1..0....1..1..1....1..0..0....0..0..1....1..0..0....0..1..0
%e A223833 ..0..1..0....1..1..1....1..1..1....1..0..0....0..1..1....1..1..1....1..1..0
%e A223833 ..1..1..0....1..1..1....1..1..1....1..0..0....1..1..1....1..1..1....1..1..1
%Y A223833 Column 3 of A223838.
%K A223833 nonn
%O A223833 1,1
%A A223833 _R. H. Hardin_, Mar 27 2013
%E A223833 Name corrected by _Andrew Howroyd_, Mar 18 2025