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A252978 Number of n X 3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down. 1
1, 1, 1, 33, 266, 851, 1836, 3221, 5006, 7191, 9776, 12761, 16146, 19931, 24116, 28701, 33686, 39071, 44856, 51041, 57626, 64611, 71996, 79781, 87966, 96551, 105536, 114921, 124706, 134891, 145476, 156461, 167846, 179631, 191816, 204401, 217386 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 200*n^2 - 1615*n + 3341 for n>4.

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

G.f.: x*(1 - 2*x + x^2 + 32*x^3 + 169*x^4 + 151*x^5 + 48*x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.

(End)

EXAMPLE

Some solutions for n=4:

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

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

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

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

CROSSREFS

Column 3 of A252983.

Sequence in context: A197398 A061223 A119782 * A268264 A008515 A179995

Adjacent sequences:  A252975 A252976 A252977 * A252979 A252980 A252981

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 25 2014

STATUS

approved

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Last modified September 28 08:13 EDT 2022. Contains 357068 sequences. (Running on oeis4.)