A250775 Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

576, 1026, 1622, 2396, 3412, 4798, 6810, 9960, 15272, 24794, 42622, 76948, 144156, 277014, 541058, 1067360, 2118064, 4217458, 8414118, 16805196, 33584996, 67142126, 134253802, 268474456, 536912952, 1073787018, 2147532110, 4295019140

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) + 7*a(n-3) - 2*a(n-4); a(n) = 32*2^(n-1) + 57*n^2 + 247*n + 240.

Empirical g.f.: 2*x*(288 - 927*x + 838*x^2 - 256*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 19 2018

Example

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

Crossrefs

Row 7 of A250769.

Sequence in context: A295017 A053969 A316486 * A109101 A258919 A064253

Adjacent sequences: A250772 A250773 A250774 * A250776 A250777 A250778

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved