A250847 Number of (n+1) X (2+1) 0..3 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.

400, 2457, 13097, 63631, 291165, 1280447, 5480917, 23024631, 95448605, 391939087, 1598379237, 6485763431, 26220548845, 105716192127, 425369781557, 1709000211031, 6858576189885, 27502054979567, 110211518943877

Offset

1,1

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (4838*4^n - 6300*3^n + 2214*2^n - 80)/12.

Empirical g.f.: x*(400 - 1543*x + 2527*x^2 - 1344*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 21 2018

Example

Some solutions for n=4:
..3..1..1....1..1..1....2..2..3....0..0..0....2..1..1....3..1..1....3..3..2
..0..0..0....3..3..3....2..2..3....1..1..1....1..1..1....1..1..1....0..0..0
..2..2..3....2..2..3....2..2..3....1..1..1....1..1..1....0..1..1....0..0..0
..0..1..3....0..0..1....2..2..3....1..2..2....0..0..0....0..2..3....0..1..2
..0..1..3....1..2..3....0..1..2....0..1..2....2..3..3....0..2..3....1..2..3

Crossrefs

Column 2 of A250853.

Sequence in context: A223481 A037991 A200837 * A043400 A038483 A250430

Adjacent sequences: A250844 A250845 A250846 * A250848 A250849 A250850

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved