A252822 Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 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, 18, 53, 142, 339, 729, 1437, 2638, 4568, 7536, 11937, 18266, 27133, 39279, 55593, 77130, 105130, 141038, 186525, 243510, 314183, 401029, 506853, 634806, 788412, 971596, 1188713, 1444578, 1744497, 2094299, 2500369, 2969682, 3509838, 4129098

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 + (7/240)*n^5 + (5/144)*n^4 - (11/48)*n^3 + (527/360)*n^2 - (3/10)*n + 1.

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

G.f.: x*(2 - 8*x + 18*x^2 - 17*x^3 + 9*x^4 - 4*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Column 2 of A252828.

Sequence in context: A077984 A052979 A005507 * A094864 A120010 A132790

Adjacent sequences: A252819 A252820 A252821 * A252823 A252824 A252825

Keyword

nonn

Author

R. H. Hardin, Dec 22 2014

Status

approved