A250725 Number of (n+1) X (4+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.

114, 257, 496, 885, 1500, 2434, 3807, 5760, 8465, 12119, 16954, 23231, 31250, 41344, 53889, 69298, 88031, 110589, 137524, 169433, 206968, 250830, 301779, 360628, 428253, 505587, 593630, 693443, 806158, 932972, 1075157, 1234054, 1411083

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7) for n>8.

Empirical for n mod 2 = 0: a(n) = (1/60)*n^5 + (13/24)*n^4 + (8/3)*n^3 + (407/24)*n^2 + (3859/60)*n + 30 for n>1.

Empirical for n mod 2 = 1: a(n) = (1/60)*n^5 + (13/24)*n^4 + (8/3)*n^3 + (407/24)*n^2 + (3859/60)*n + (61/2) for n>1.

Empirical g.f.: x*(114 - 313*x + 237*x^2 + 148*x^3 - 316*x^4 + 160*x^5 - 25*x^6 - x^7) / ((1 - x)^6*(1 + x)). - Colin Barker, Nov 16 2018

Example

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

Crossrefs

Column 4 of A250729.

Sequence in context: A160776 A171374 A228962 * A300478 A305066 A322541

Adjacent sequences: A250722 A250723 A250724 * A250726 A250727 A250728

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved