A250579 Number of (n+1) X (4+1) 0..1 arrays with nondecreasing max(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.

125, 329, 778, 1776, 4013, 9055, 20510, 46664, 106695, 244907, 564056, 1302196, 3011939, 6975231, 16168980, 37503362, 87027117, 202004681, 468985712, 1088963192, 2528765147, 5872573601, 13638522600, 31675031834, 73565690547

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 10*a(n-2) - 7*a(n-3) + 40*a(n-4) - 40*a(n-5) - 2*a(n-6) + 29*a(n-7) - 19*a(n-8) + 4*a(n-9) for n>10.

Empirical g.f.: x*(125 - 421*x + 54*x^2 + 1273*x^3 - 1560*x^4 + 23*x^5 + 1032*x^6 - 642*x^7 + 106*x^8 + 8*x^9) / ((1 - x)^4*(1 - 2*x - 4*x^2 + 7*x^3 + 3*x^4 - 4*x^5)). - Colin Barker, Nov 15 2018

Example

Some solutions for n=6:
..0..1..0..1..0....1..0..0..1..1....1..0..0..0..0....0..0..0..1..1
..1..0..1..0..1....0..1..1..1..1....0..1..0..1..1....0..0..1..0..1
..0..1..0..1..1....1..0..1..1..1....1..0..1..0..1....0..1..0..1..1
..1..0..1..1..1....0..1..0..1..1....0..1..0..1..0....1..0..1..1..1
..0..1..1..1..1....1..0..1..1..1....1..0..1..0..1....0..1..1..1..1
..0..1..1..1..1....0..1..0..1..1....0..1..0..1..1....0..1..1..1..1
..0..1..1..1..1....1..0..1..1..1....1..0..1..0..1....0..1..1..1..1

Crossrefs

Column 4 of A250583.

Sequence in context: A223182 A256362 A175486 * A161855 A353502 A252057

Adjacent sequences: A250576 A250577 A250578 * A250580 A250581 A250582

Keyword

nonn

Author

R. H. Hardin, Nov 25 2014

Status

approved