A252814 Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

2, 6, 17, 40, 81, 147, 246, 387, 580, 836, 1167, 1586, 2107, 2745, 3516, 4437, 5526, 6802, 8285, 9996, 11957, 14191, 16722, 19575, 22776, 26352, 30331, 34742, 39615, 44981, 50872, 57321, 64362, 72030, 80361, 89392, 99161, 109707, 121070, 133291

Offset: 1

Author

R. H. Hardin, Dec 22 2014

Keywords

• nonn

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• W. Kuszmaul, Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in Permutations, arXiv preprint arXiv:1509.08216 [cs.DM], 2015-2017.

Crossrefs

Column 2 of A252820.

Formula

Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 - (1/24)*n^2 + (7/12)*n + 1.

Conjectures from Colin Barker, Dec 06 2018: (Start)

G.f.: x*(2 - 4*x + 7*x^2 - 5*x^3 + 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)