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A252831 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 2 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, 127, 288, 529, 850, 1251, 1732, 2293, 2934, 3655, 4456, 5337, 6298, 7339, 8460, 9661, 10942, 12303, 13744, 15265, 16866, 18547, 20308, 22149, 24070, 26071, 28152, 30313, 32554, 34875, 37276, 39757, 42318, 44959, 47680, 50481, 53362, 56323 (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) = 40*n^2 - 199*n + 283 for n>3.

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

G.f.: x*(4 + x + 17*x^2 + 30*x^3 + 26*x^4 + 2*x^5) / (1 - x)^3.

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

(End)

EXAMPLE

Some solutions for n=4:

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

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

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

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

CROSSREFS

Column 3 of A252836.

Sequence in context: A149426 A042767 A286175 * A219708 A345230 A117882

Adjacent sequences:  A252828 A252829 A252830 * A252832 A252833 A252834

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 22 2014

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)