A253395 Number of (n+1) X (6+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.

476, 320, 419, 632, 932, 1318, 1855, 2528, 3408, 4498, 5864, 7521, 9542, 11949, 14824, 18197, 22158, 26745, 32056, 38137, 45094, 52981, 61912, 71949, 83214, 95777, 109768, 125265, 142406, 161277, 182024, 204741, 229582, 256649, 286104, 318057

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6) for n>16.

Empirical for n mod 2 = 0: a(n) = (1/6)*n^4 + (185/6)*n^2 - 61*n + 357 for n>10.

Empirical for n mod 2 = 1: a(n) = (1/6)*n^4 + (185/6)*n^2 - 61*n + 364 for n>10.

Empirical g.f.: x*(476 - 1584*x + 1519*x^2 + 556*x^3 - 1881*x^4 + 1054*x^5 - 48*x^6 - 106*x^7 + 20*x^8 + 12*x^9 - 23*x^10 + 17*x^11 - 5*x^12 + 2*x^14 - x^15) / ((1 - x)^5*(1 + x)). - Colin Barker, Dec 12 2018

Example

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

Crossrefs

Column 6 of A253397.

Sequence in context: A210048 A263705 A048428 * A171077 A234077 A205287

Adjacent sequences: A253392 A253393 A253394 * A253396 A253397 A253398

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved