A253507 Number of (n+2) X (5+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.

884, 1712, 3052, 5136, 7948, 11740, 16592, 22720, 30300, 39560, 50740, 64104, 79936, 98540, 120240, 145380, 174324, 207456, 245180, 287920, 336120, 390244, 450776, 518220, 593100, 675960, 767364, 867896, 978160, 1098780, 1230400, 1373684

Offset

1,1

Links

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

Formula

Empirical: a(n) = (5/6)*n^4 + 9*n^3 + (1135/6)*n^2 + 361*n - 300 for n>8.

Conjectures from Colin Barker, Dec 17 2018: (Start)

G.f.: 4*x*(221 - 677*x + 833*x^2 - 461*x^3 + 22*x^4 + 129*x^5 - 110*x^6 + 77*x^7 - 44*x^8 + 23*x^9 - 10*x^10 + 3*x^11 - x^12) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>13.

(End)

Example

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

Crossrefs

Column 5 of A253510.

Sequence in context: A206964 A209089 A207131 * A282156 A318200 A295443

Adjacent sequences: A253504 A253505 A253506 * A253508 A253509 A253510

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved