A252815 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

4, 17, 63, 187, 468, 1032, 2067, 3840, 6716, 11179, 17855, 27537, 41212, 60090, 85635, 119598, 164052, 221429, 294559, 386711, 501636, 643612, 817491, 1028748, 1283532, 1588719, 1951967, 2381773, 2887532, 3479598, 4169347, 4969242, 5892900, 6955161

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/360)*n^6 + (1/20)*n^5 + (5/18)*n^4 + (1/2)*n^3 + (439/360)*n^2 - (1/20)*n + 2.

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

G.f.: x*(4 - 11*x + 28*x^2 - 37*x^3 + 27*x^4 - 11*x^5 + 2*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=4:
..0..0..1....0..0..0....0..1..1....0..0..1....0..1..2....0..1..2....0..1..1
..0..0..1....1..1..1....1..2..2....1..1..2....1..2..2....1..2..3....0..1..1
..1..1..2....1..1..2....2..2..3....1..2..2....2..3..3....1..2..3....1..1..2
..1..2..3....2..2..3....2..3..4....1..2..3....2..3..3....1..2..3....2..2..3

Crossrefs

Column 3 of A252820.

Sequence in context: A202752 A286210 A339286 * A362593 A191272 A122231

Adjacent sequences: A252812 A252813 A252814 * A252816 A252817 A252818

Keyword

nonn

Author

R. H. Hardin, Dec 22 2014

Status

approved