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A253391 Number of (n+1) X (2+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 A253391 #7 Dec 11 2018 08:42:03
%S A253391 44,102,143,197,250,320,391,477,564,666,769,887,1006,1140,1275,1425,
%T A253391 1576,1742,1909,2091,2274,2472,2671,2885,3100,3330,3561,3807,4054,
%U A253391 4316,4579,4857,5136,5430,5725,6035,6346,6672,6999,7341,7684,8042,8401,8775,9150
%N A253391 Number of (n+1) X (2+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 A253391 R. H. Hardin, <a href="/A253391/b253391.txt">Table of n, a(n) for n = 1..210</a>
%F A253391 Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>8.
%F A253391 Empirical for n mod 2 = 0: a(n) = 4*n^2 + (45/2)*n + 41 for n>4.
%F A253391 Empirical for n mod 2 = 1: a(n) = 4*n^2 + (45/2)*n + (75/2) for n>4.
%F A253391 Empirical g.f.: x*(44 + 14*x - 61*x^2 - x^3 + 16*x^4 + 4*x^5 + 2*x^6 - 2*x^7) / ((1 - x)^3*(1 + x)). - _Colin Barker_, Dec 11 2018
%e A253391 Some solutions for n=4:
%e A253391 ..1..1..1....1..1..1....0..1..1....1..1..1....1..1..1....0..1..0....1..0..1
%e A253391 ..1..1..1....1..1..0....0..0..0....1..1..0....0..1..0....1..1..0....0..0..0
%e A253391 ..1..1..0....1..1..1....0..0..1....0..1..0....0..1..0....1..1..0....0..1..0
%e A253391 ..0..1..0....0..0..0....0..0..1....0..1..0....0..1..0....1..1..1....0..1..0
%e A253391 ..0..1..0....0..1..1....0..0..1....0..1..0....0..1..0....1..0..0....0..1..0
%Y A253391 Column 2 of A253397.
%K A253391 nonn
%O A253391 1,1
%A A253391 _R. H. Hardin_, Dec 31 2014