A250786 Number of (4+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.

72, 196, 482, 1152, 2640, 5882, 12796, 27344, 57610, 120060, 248072, 509158, 1039532, 2113580, 4283210, 8657344, 17462056, 35162842, 70712260, 142050352, 285113682, 571866796, 1146386672, 2297066582, 4601080260, 9213401692

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 11*a(n-4) - 5*a(n-5) - 3*a(n-6) + 2*a(n-7).

Empirical g.f.: 2*x*(36 - 82*x + 3*x^2 + 129*x^3 - 73*x^4 - 43*x^5 + 32*x^6) / ((1 - x)^3*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

Example

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

Crossrefs

Row 4 of A250783.

Sequence in context: A304376 A028977 A033693 * A302886 A235186 A235179

Adjacent sequences: A250783 A250784 A250785 * A250787 A250788 A250789

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved