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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
OFFSET
1,4
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 25 2014
STATUS
approved