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A253001 Number of n X 5 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down. 1
4, 14, 34, 69, 69, 3072, 39758, 228484, 775433, 1932763, 3965261, 7139167, 11720721, 17976163, 26171733, 36573671, 49448217, 65061611, 83680093, 105569903, 130997281, 160228467, 193529701, 231167223, 273407273, 320516091, 372759917 (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) = (133120/3)*n^3 - 893616*n^2 + (18332582/3)*n - 14187577 for n>8.

Conjectures from Colin Barker, Dec 08 2018: (Start)

G.f.: x*(4 - 2*x + 2*x^2 + x^3 - 55*x^4 + 3088*x^5 + 27642*x^6 + 87677*x^7 + 87826*x^8 + 45975*x^9 + 12629*x^10 + 1453*x^11) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>12.

(End)

EXAMPLE

Some solutions for n=6:

..0..0..0..1..2....0..0..0..1..2....0..0..0..0..1....0..0..1..1..1

..1..1..1..1..2....0..1..1..1..2....0..0..1..1..1....0..0..1..1..1

..1..1..2..2..2....1..1..1..1..2....0..1..1..1..1....1..1..1..2..2

..1..2..2..2..2....1..1..1..1..2....1..1..1..1..2....1..1..1..2..2

..1..2..2..2..2....2..2..2..2..2....1..1..1..2..2....2..2..2..2..2

..2..2..2..2..2....2..2..2..2..2....2..2..2..2..2....2..2..2..2..2

CROSSREFS

Column 5 of A253004.

Sequence in context: A098942 A011554 A099586 * A063258 A178964 A197275

Adjacent sequences:  A252998 A252999 A253000 * A253002 A253003 A253004

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 25 2014

STATUS

approved

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Last modified February 22 18:05 EST 2019. Contains 320400 sequences. (Running on oeis4.)