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, 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

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