A253394 Number of (n+1) X (5+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.

304, 250, 316, 465, 666, 932, 1269, 1693, 2201, 2814, 3527, 4360, 5309, 6394, 7611, 8980, 10497, 12182, 14031, 16064, 18277, 20690, 23299, 26124, 29161, 32430, 35927, 39672, 43661, 47914, 52427, 57220, 62289, 67654, 73311, 79280, 85557, 92162, 99091

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>13.

Empirical for n mod 2 = 0: a(n) = (4/3)*n^3 + 13*n^2 + (5/3)*n + 164 for n>8.

Empirical for n mod 2 = 1: a(n) = (4/3)*n^3 + 13*n^2 + (5/3)*n + 161 for n>8.

Empirical g.f.: x*(304 - 662*x + 174*x^2 + 625*x^3 - 509*x^4 + 50*x^5 + 37*x^6 + 3*x^7 - 9*x^8 + 5*x^9 - 2*x^10 - x^11 + x^12) / ((1 - x)^4*(1 + x)). - Colin Barker, Dec 12 2018

Example

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

Crossrefs

Column 5 of A253397.

Sequence in context: A332130 A291132 A328277 * A214608 A158932 A270303

Adjacent sequences: A253391 A253392 A253393 * A253395 A253396 A253397

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved