A250724 Number of (n+1) X (3+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.

50, 110, 208, 365, 600, 942, 1418, 2065, 2918, 4022, 5420, 7165, 9308, 11910, 15030, 18737, 23098, 28190, 34088, 40877, 48640, 57470, 67458, 78705, 91310, 105382, 121028, 138365, 157508, 178582, 201710, 227025, 254658, 284750, 317440, 352877

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) = (1/6)*n^4 + (4/3)*n^3 + (91/12)*n^2 + (74/3)*n + 17.

Empirical for n mod 2 = 1: a(n) = (1/6)*n^4 + (4/3)*n^3 + (91/12)*n^2 + (74/3)*n + (65/4).

Empirical g.f.: x*(50 - 90*x + 18*x^2 + 83*x^3 - 70*x^4 + 17*x^5) / ((1 - x)^5*(1 + x)). - Colin Barker, Nov 16 2018

Example

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

Crossrefs

Column 3 of A250729.

Sequence in context: A039397 A044000 A256631 * A044237 A044618 A248531

Adjacent sequences: A250721 A250722 A250723 * A250725 A250726 A250727

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved