A252871 Number of nX3 nonnegative integer arrays with upper left 0 and lower right n+3-4 and value increasing by 0 or 1 with every step right or down

1, 8, 44, 153, 413, 949, 1948, 3676, 6497, 10894, 17492, 27083, 40653, 59411, 84820, 118630, 162913, 220100, 293020, 384941, 499613, 641313, 814892, 1025824, 1280257, 1585066, 1947908, 2377279, 2882573, 3474143, 4163364, 4962698, 5885761, 6947392

Offset

1,2

Comments

Column 3 of A252876

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 + (1/3)*n^3 + (79/360)*n^2 - (113/60)*n + 2.

Empirical: G.f.: -x*(1+x+9*x^2-22*x^3+21*x^4-10*x^5+2*x^6) / (x-1)^7. - R. J. Mathar, Nov 23 2015

Example

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

Crossrefs

Sequence in context: A261996 A036464 A000938 * A307044 A165618 A250285

Adjacent sequences: A252868 A252869 A252870 * A252872 A252873 A252874

Keyword

nonn

Author

R. H. Hardin, Dec 24 2014

Status

approved