A228255 Number of third differences of arrays of length n+3 of numbers in 0..3.

25, 319, 2511, 13933, 58911, 242461, 989527, 4017157, 16245775, 65514541, 263652487, 1059392917, 4251920575, 17050729021, 68332056247, 273715645477, 1096024843375, 4387586157901, 17560804984807, 70274600998837

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 12*a(n-2) for n>7.

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

G.f.: x*(25 + 144*x + 578*x^2 + 184*x^3 - 8488*x^4 - 2720*x^5 - 768*x^6) / ((1 - 3*x)*(1 - 4*x)).

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

(End)

Example

Some solutions for n=4:
.-7....4....0...-5...-5..-12....5....1..-11...-1....7...-5....6....3....8...-3
.10...-1....0....7....1...10..-10....1....9....1...-1....4...-9...-1...-8....5
.-9...-3...-6....0...-1...-6....9....2....0...-3...-4....3....7....2....3..-10
..6....1....9...-8....5....4...-3...-2...-7....4....6...-9...-2...-7....4...12

Crossrefs

Column 3 of A228260.

Sequence in context: A278876 A053805 A240846 * A125437 A250318 A250559

Adjacent sequences: A228252 A228253 A228254 * A228256 A228257 A228258

Keyword

nonn

Author

R. H. Hardin, Aug 19 2013

Status

approved