A250732 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 min(x(i,j),x(i-1,j)) in the j direction.

33, 85, 208, 496, 1158, 2699, 6257, 14520, 33640, 77999, 180744, 419005, 971109, 2251135, 5217807, 12095192, 28036004, 64988500, 150642356, 349192782, 809429294, 1876272631, 4349215350, 10081551668, 23369149689, 54170034264

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 9*a(n-3) + 12*a(n-4) - 2*a(n-5) - 3*a(n-6) + a(n-7) for n>8.

Empirical g.f.: x*(33 - 47*x - 66*x^2 + 131*x^3 - 41*x^4 - 23*x^5 + 14*x^6 - 2*x^7) / ((1 - x)^2*(1 - 2*x - 3*x^2 + 5*x^3 + x^4 - x^5)). - Colin Barker, Nov 16 2018

Example

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

Crossrefs

Row 3 of A250729.

Sequence in context: A359746 A039833 A355711 * A080700 A292366 A080200

Adjacent sequences: A250729 A250730 A250731 * A250733 A250734 A250735

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved