A252980 Number of n X 5 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.

6, 41, 266, 1247, 4657, 67537, 433401, 1481460, 3510600, 6637020, 10878576, 16235268, 22707096, 30294060, 38996160, 48813396, 59745768, 71793276, 84955920, 99233700, 114626616, 131134668, 148757856, 167496180, 187349640, 208318236

Offset

1,1

Comments

Column 5 of A252983.

Links

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

Formula

Empirical: a(n) = 557568*n^2 - 7467372*n + 25553940 for n>8.

Conjectures from Colin Barker, Mar 20 2018: (Start)

G.f.: x*(6 + 23*x + 161*x^2 + 566*x^3 + 1673*x^4 + 57041*x^5 + 243514*x^6 + 379211*x^7 + 298886*x^8 + 116199*x^9 + 17856*x^10) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.

(End)

Example

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

Crossrefs

Cf. A252983.

Sequence in context: A266425 A194781 A323969 * A274997 A015551 A291018

Adjacent sequences: A252977 A252978 A252979 * A252981 A252982 A252983

Keyword

nonn

Author

R. H. Hardin, Dec 25 2014

Status

approved