A252832 Number of n X 4 nonnegative integer arrays with upper left 0 and every value within 2 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

7, 29, 127, 493, 1474, 3365, 6211, 10017, 14783, 20509, 27195, 34841, 43447, 53013, 63539, 75025, 87471, 100877, 115243, 130569, 146855, 164101, 182307, 201473, 221599, 242685, 264731, 287737, 311703, 336629, 362515, 389361, 417167, 445933

Offset

1,1

Links

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

Formula

Empirical: a(n) = 480*n^2 - 3394*n + 6449 for n>5.

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

G.f.: x*(7 + 8*x + 61*x^2 + 192*x^3 + 347*x^4 + 295*x^5 + 45*x^6 + 5*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)

Example

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

Crossrefs

Column 4 of A252836.

Sequence in context: A055427 A048876 A126394 * A074468 A303091 A333887

Adjacent sequences: A252829 A252830 A252831 * A252833 A252834 A252835

Keyword

nonn

Author

R. H. Hardin, Dec 22 2014

Status

approved