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A252933 Number of n X 3 nonnegative integer arrays with upper left 0 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, 13, 44, 153, 494, 1343, 3016, 5833, 10114, 16179, 24348, 34941, 48278, 64679, 84464, 107953, 135466, 167323, 203844, 245349, 292158, 344591, 402968, 467609, 538834, 616963, 702316, 795213, 895974, 1004919, 1122368, 1248641, 1384058 (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) = (160/3)*n^3 - 548*n^2 + (6071/3)*n - 2591 for n>4.

Conjectures from Colin Barker, Dec 07 2018: (Start)

G.f.: x*(4 - 3*x + 16*x^2 + 39*x^3 + 98*x^4 + 122*x^5 + 40*x^6 + 4*x^7) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.

(End)

EXAMPLE

Some solutions for n=4:

..0..0..0....0..0..1....0..1..1....0..0..1....0..0..0....0..0..0....0..0..0

..0..0..1....1..1..1....1..1..1....0..1..1....0..0..0....0..0..1....0..0..1

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

..0..1..1....1..2..2....2..2..3....1..1..2....1..1..1....1..1..1....1..1..2

CROSSREFS

Column 3 of A252938.

Sequence in context: A073717 A149427 A290907 * A229397 A283110 A149428

Adjacent sequences:  A252930 A252931 A252932 * A252934 A252935 A252936

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 24 2014

STATUS

approved

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Last modified March 30 21:56 EDT 2020. Contains 333132 sequences. (Running on oeis4.)