A250625 Number of (n+1) X (1+1) 0..2 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.

36, 125, 380, 1072, 2856, 7307, 18131, 43966, 104755, 246252, 572894, 1322172, 3032579, 6922433, 15743520, 35703349, 80791394, 182511840, 411772666, 928103255, 2090301223, 4705147230, 10586418861, 23811245592, 53543550752

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + a(n-3) + 16*a(n-4) - 10*a(n-5) - 7*a(n-6) + 6*a(n-7) + a(n-8) - a(n-9).

Empirical g.f.: x*(36 - 91*x + 26*x^2 + 131*x^3 - 97*x^4 - 57*x^5 + 55*x^6 + 8*x^7 - 9*x^8) / ((1 - x)^2*(1 - x - x^2)^2*(1 - 2*x - x^2 + x^3)). - Colin Barker, Nov 15 2018

Example

Some solutions for n=4:
..0..0....0..0....1..0....1..0....0..0....0..0....1..0....0..1....0..0....0..1
..1..1....1..1....0..1....0..1....0..1....0..0....0..2....1..0....1..1....1..0
..0..2....1..1....1..0....0..1....1..0....1..0....1..1....0..2....0..2....0..1
..0..2....1..1....0..2....1..0....0..1....0..2....1..2....1..1....0..2....0..1
..1..2....1..1....2..0....0..1....1..2....0..2....2..2....1..1....1..1....0..1

Crossrefs

Column 1 of A250632.

Sequence in context: A238037 A238032 A365506 * A057837 A352316 A007265

Adjacent sequences: A250622 A250623 A250624 * A250626 A250627 A250628

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved