A228256 Number of third differences of arrays of length n+3 of numbers in 0..4.

33, 565, 6419, 53315, 315601, 1688101, 8717049, 44633821, 227363409, 1153594261, 5835080169, 29443836301, 148292923329, 745759583941, 3745977788889, 18798608421181, 94267920012849, 472439111692021, 2366593604971209

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..121

Formula

Empirical: a(n) = 9*a(n-1) - 20*a(n-2) for n>8.

Conjectures from Colin Barker, Sep 10 2018: (Start)

G.f.: x*(33 + 268*x + 1994*x^2 + 6844*x^3 - 35854*x^4 - 86008*x^5 - 163840*x^6 - 57600*x^7) / ((1 - 4*x)*(1 - 5*x)).

a(n) = 5^(3+n) - 4^(3+n) for n>6.

(End)

Example

Some solutions for n=4:
.12..-10....2...-7....8...-5....2..-13...-7..-15...-6...-3....5....3....7....2
.-7....8....3....6...-2....1....0...13....4....9....0....4...-2...-3..-12....3
.-1...-6....1....1...-1...-3...-7..-12....1....0....9...-1...-6....2...12...-1
..4....8...-7...-1...-4...-2...10...12...-6...-2..-13...-3...10...-5...-6....5

Crossrefs

Column 4 of A228260.

Sequence in context: A188357 A126923 A010985 * A197361 A282926 A172362

Adjacent sequences: A228253 A228254 A228255 * A228257 A228258 A228259

Keyword

nonn

Author

R. H. Hardin, Aug 19 2013

Status

approved