A250723 Number of (n+1) X (2+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.

22, 46, 85, 144, 230, 350, 513, 728, 1006, 1358, 1797, 2336, 2990, 3774, 4705, 5800, 7078, 8558, 10261, 12208, 14422, 16926, 19745, 22904, 26430, 30350, 34693, 39488, 44766, 50558, 56897, 63816, 71350, 79534, 88405, 98000, 108358, 119518, 131521

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).

Empirical for n mod 2 = 0: a(n) = (1/24)*n^4 + (1/2)*n^3 + (10/3)*n^2 + 10*n + 8.

Empirical for n mod 2 = 1: a(n) = (1/24)*n^4 + (1/2)*n^3 + (10/3)*n^2 + 10*n + (65/8).

Empirical g.f.: x*(22 - 42*x + 11*x^2 + 34*x^3 - 31*x^4 + 8*x^5) / ((1 - x)^5*(1 + x)). - Colin Barker, Nov 16 2018

Example

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

Crossrefs

Column 2 of A250729.

Sequence in context: A158862 A161666 A132763 * A044099 A044480 A253602

Adjacent sequences: A250720 A250721 A250722 * A250724 A250725 A250726

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved