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.

96, 143, 174, 246, 316, 419, 520, 651, 780, 939, 1096, 1283, 1468, 1683, 1896, 2139, 2380, 2651, 2920, 3219, 3516, 3843, 4168, 4523, 4876, 5259, 5640, 6051, 6460, 6899, 7336, 7803, 8268, 8763, 9256, 9779, 10300, 10851, 11400, 11979, 12556, 13163, 13768

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

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

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

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

Example

Some solutions for n=4:
..0..0..0..0....0..0..0..0....1..1..0..0....1..0..0..1....0..0..0..1
..0..0..0..0....0..0..0..0....1..1..1..1....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..1..0....1..0..0..0....1..1..1..1....0..0..0..0
..0..0..0..0....0..0..1..0....1..1..1..1....0..0..0..0....0..0..1..0
..1..1..1..1....1..0..1..0....0..0..0..0....1..1..1..1....0..0..1..0

Crossrefs

Column 3 of A253397.

Sequence in context: A146992 A261287 A252689 * A116119 A039600 A143847

Adjacent sequences: A253389 A253390 A253391 * A253393 A253394 A253395

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved