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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. 1

%I #7 Dec 11 2018 08:58:29

%S 96,143,174,246,316,419,520,651,780,939,1096,1283,1468,1683,1896,2139,

%T 2380,2651,2920,3219,3516,3843,4168,4523,4876,5259,5640,6051,6460,

%U 6899,7336,7803,8268,8763,9256,9779,10300,10851,11400,11979,12556,13163,13768

%N 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 R. H. Hardin, <a href="/A253392/b253392.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>8.

%F Empirical for n mod 2 = 0: a(n) = 7*n^2 + 18*n + 59 for n>4.

%F Empirical for n mod 2 = 1: a(n) = 7*n^2 + 18*n + 51 for n>4.

%F 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 Some solutions for n=4:

%e ..0..0..0..0....0..0..0..0....1..1..0..0....1..0..0..1....0..0..0..1

%e ..0..0..0..0....0..0..0..0....1..1..1..1....0..0..0..0....0..0..0..0

%e ..0..0..0..0....0..0..1..0....1..0..0..0....1..1..1..1....0..0..0..0

%e ..0..0..0..0....0..0..1..0....1..1..1..1....0..0..0..0....0..0..1..0

%e ..1..1..1..1....1..0..1..0....0..0..0..0....1..1..1..1....0..0..1..0

%Y Column 3 of A253397.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 31 2014

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)