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A253392 Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

%I A253392 #7 Dec 11 2018 08:58:29
%S A253392 96,143,174,246,316,419,520,651,780,939,1096,1283,1468,1683,1896,2139,
%T A253392 2380,2651,2920,3219,3516,3843,4168,4523,4876,5259,5640,6051,6460,
%U A253392 6899,7336,7803,8268,8763,9256,9779,10300,10851,11400,11979,12556,13163,13768
%N A253392 Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.
%H A253392 R. H. Hardin, <a href="/A253392/b253392.txt">Table of n, a(n) for n = 1..210</a>
%F A253392 Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>8.
%F A253392 Empirical for n mod 2 = 0: a(n) = 7*n^2 + 18*n + 59 for n>4.
%F A253392 Empirical for n mod 2 = 1: a(n) = 7*n^2 + 18*n + 51 for n>4.
%F A253392 Empirical g.f.: x*(96 - 49*x - 112*x^2 + 90*x^3 + 14*x^4 - 8*x^5 - 3*x^7) / ((1 - x)^3*(1 + x)). - _Colin Barker_, Dec 11 2018
%e A253392 Some solutions for n=4:
%e A253392 ..0..0..0..0....0..0..0..0....1..1..0..0....1..0..0..1....0..0..0..1
%e A253392 ..0..0..0..0....0..0..0..0....1..1..1..1....0..0..0..0....0..0..0..0
%e A253392 ..0..0..0..0....0..0..1..0....1..0..0..0....1..1..1..1....0..0..0..0
%e A253392 ..0..0..0..0....0..0..1..0....1..1..1..1....0..0..0..0....0..0..1..0
%e A253392 ..1..1..1..1....1..0..1..0....0..0..0..0....1..1..1..1....0..0..1..0
%Y A253392 Column 3 of A253397.
%K A253392 nonn
%O A253392 1,1
%A A253392 _R. H. Hardin_, Dec 31 2014