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A228255
Number of third differences of arrays of length n+3 of numbers in 0..3.
1
25, 319, 2511, 13933, 58911, 242461, 989527, 4017157, 16245775, 65514541, 263652487, 1059392917, 4251920575, 17050729021, 68332056247, 273715645477, 1096024843375, 4387586157901, 17560804984807, 70274600998837
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 19 2013
STATUS
approved