A252935 Number of n X 5 nonnegative integer arrays with upper left 0 and every value within 3 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.

15, 83, 494, 3067, 17962, 86488, 320270, 917811, 2127013, 4211511, 7437417, 12070971, 18378413, 26625983, 37079921, 50006467, 65671861, 84342343, 106284153, 131763531, 161046717, 194399951, 232089473, 274381523, 321542341

Offset

1,1

Links

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

Formula

Empirical: a(n) = (133120/3)*n^3 - 760496*n^2 + (13526246/3)*n - 9199709 for n>8.

Conjectures from Colin Barker, Dec 07 2018: (Start)

G.f.: x*(15 + 23*x + 252*x^2 + 1529*x^3 + 8341*x^4 + 31149*x^5 + 70316*x^6 + 86878*x^7 + 49399*x^8 + 15733*x^9 + 2477*x^10 + 128*x^11) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>12.

(End)

Example

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

Crossrefs

Column 5 of A252938.

Sequence in context: A065103 A279395 A270768 * A247958 A108674 A050405

Adjacent sequences: A252932 A252933 A252934 * A252936 A252937 A252938

Keyword

nonn

Author

R. H. Hardin, Dec 24 2014

Status

approved