A250849 Number of (n+1) X (4+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.

3136, 21436, 123016, 626416, 2955136, 13263136, 57570016, 244213216, 1019415136, 4206874336, 17218194016, 70050978016, 283750743136, 1145667917536, 4614715410016, 18555090670816, 74509245399136, 298904020992736

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) = (52650*4^n - 80640*3^n + 35820*2^n - 2688)/12.

Empirical g.f.: 4*x*(784 - 2481*x + 4604*x^2 - 2571*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 21 2018

Example

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

Crossrefs

Column 4 of A250853.

Sequence in context: A071143 A284984 A061048 * A238499 A176790 A086103

Adjacent sequences: A250846 A250847 A250848 * A250850 A250851 A250852

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved