A253001 - OEIS

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.

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

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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: A370838 A366086 A099586 * A348309 A063258 A178964

Adjacent sequences: A252998 A252999 A253000 * A253002 A253003 A253004

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 25 2014

STATUS

approved