A250726 Number of (n+1) X (5+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

257, 596, 1158, 2092, 3605, 6016, 9728, 15297, 23407, 34943, 50970, 72810, 102025, 140498, 190420, 254375, 335331, 436729, 562478, 717048, 905469, 1133428, 1407272, 1734109, 2121815, 2579139, 3115714, 3742166, 4470129, 5312358, 6282748, 7396451

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8) for n>10.

Empirical for n mod 2 = 0: a(n) = (1/360)*n^6 + (1/12)*n^5 + (49/36)*n^4 + (13/3)*n^3 + (15169/360)*n^2 + (1957/12)*n + 43 for n>2.

Empirical for n mod 2 = 1: a(n) = (1/360)*n^6 + (1/12)*n^5 + (49/36)*n^4 + (13/3)*n^3 + (15169/360)*n^2 + (1957/12)*n + 40 for n>2.

Empirical g.f.: x*(257 - 946*x + 1180*x^2 - 110*x^3 - 1079*x^4 + 1060*x^5 - 440*x^6 + 93*x^7 - 12*x^8 + x^9) / ((1 - x)^7*(1 + x)). - Colin Barker, Nov 16 2018

Example

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

Crossrefs

Column 5 of A250729.

Sequence in context: A095321 A100633 A007765 * A142291 A208177 A229855

Adjacent sequences: A250723 A250724 A250725 * A250727 A250728 A250729

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved