A228262 Number of third differences of arrays of length 6 of numbers in 0..n.

63, 621, 2511, 6419, 12947, 22727, 36471, 54851, 78539, 108207, 144527, 188171, 239811, 300119, 369767, 449427, 539771, 641471, 755199, 881627, 1021427, 1175271, 1343831, 1527779, 1727787, 1944527, 2178671, 2430891, 2701859, 2992247, 3302727

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..128

Formula

Empirical: a(n) = 112*n^3 - 34*n^2 - 38*n - 13 for n>4.

Conjectures from Colin Barker, Sep 11 2018: (Start)

G.f.: x*(63 + 369*x + 405*x^2 - 151*x^3 - 84*x^4 + 30*x^5 + 80*x^6 - 40*x^7) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.

(End)

Example

Some solutions for n=4:
..2...-9...-2....3....2..-12....7..-16..-10...-5....7....1....0...15...-1....0
..7....4...-5....1...-4...13...-1...12...12....7..-10....5...-5..-10....8...-7
.-8....3....3...-7....2..-14....2...-1..-12..-10....4...-8...11....4...-9....3

Crossrefs

Row 3 of A228260.

Sequence in context: A217264 A179537 A184448 * A340902 A181125 A228221

Adjacent sequences: A228259 A228260 A228261 * A228263 A228264 A228265

Keyword

nonn

Author

R. H. Hardin, Aug 19 2013

Status

approved