A250814 Number of (2+1) X (n+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.

129, 379, 873, 1731, 3097, 5139, 8049, 12043, 17361, 24267, 33049, 44019, 57513, 73891, 93537, 116859, 144289, 176283, 213321, 255907, 304569, 359859, 422353, 492651, 571377, 659179, 756729, 864723, 983881, 1114947, 1258689, 1415899

Offset

1,1

Links

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

Formula

Empirical: a(n) = 1*n^4 + 10*n^3 + 37*n^2 + 54*n + 27.

Conjectures from Colin Barker, Nov 21 2018: (Start)

G.f.: x*(129 - 266*x + 268*x^2 - 134*x^3 + 27*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Row 2 of A250812.

Sequence in context: A235879 A157951 A043383 * A249679 A250750 A036548

Adjacent sequences: A250811 A250812 A250813 * A250815 A250816 A250817

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved