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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 04:59 EST 2022. Contains 350374 sequences. (Running on oeis4.)