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A253396 Number of (n+1)X(7+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

%I A253396 #6 Jul 23 2025 14:01:43
%S A253396 704,391,520,823,1269,1855,2726,3810,5311,7163,9569,12493,16140,20493,
%T A253396 25773,31978,39346,47891,57867,69304,82472,97417,114425,133558,155118,
%U A253396 179183,206071,235876,268932,305349,345477,389442,437610,490123,547363
%N A253396 Number of (n+1)X(7+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.
%C A253396 Column 7 of A253397
%H A253396 R. H. Hardin, <a href="/A253396/b253396.txt">Table of n, a(n) for n = 1..210</a>
%F A253396 Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6) for n>18
%F A253396 Empirical for n mod 2 = 0: a(n) = (1/3)*n^4 - (1/3)*n^3 + (337/6)*n^2 - (1423/6)*n + 914 for n>12
%F A253396 Empirical for n mod 2 = 1: a(n) = (1/3)*n^4 - (1/3)*n^3 + (337/6)*n^2 - (1423/6)*n + 943 for n>12
%e A253396 Some solutions for n=4
%e A253396 ..0..0..0..0..0..0..0..1....1..1..1..1..1..1..0..1....1..1..1..0..0..0..0..1
%e A253396 ..0..0..0..0..0..0..1..0....1..1..1..1..1..1..0..0....1..1..1..1..1..1..1..1
%e A253396 ..0..0..0..0..0..0..1..0....1..1..1..1..1..1..1..1....1..0..0..0..0..0..0..0
%e A253396 ..0..0..0..0..0..0..1..0....1..1..1..1..1..0..0..0....1..1..1..1..1..1..1..1
%e A253396 ..0..0..0..0..0..0..1..0....1..1..1..1..1..1..1..1....0..0..0..0..0..0..0..0
%K A253396 nonn
%O A253396 1,1
%A A253396 _R. H. Hardin_, Dec 31 2014