A250771 Number of (3+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.

36, 66, 114, 196, 344, 622, 1158, 2208, 4284, 8410, 16634, 33052, 65856, 131430, 262542, 524728, 1049060, 2097682, 4194882, 8389236, 16777896, 33555166, 67109654, 134218576, 268436364, 536871882, 1073742858, 2147484748, 4294968464

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) = 16*2^(n-1) + n^2 + 11*n + 8.

Empirical g.f.: 2*x*(3 - 2*x)*(6 - 15*x + 8*x^2) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 19 2018

Example

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

Crossrefs

Row 3 of A250769.

Sequence in context: A126789 A176623 A211724 * A068144 A182428 A208128

Adjacent sequences: A250768 A250769 A250770 * A250772 A250773 A250774

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved