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A228213 Number of second differences of arrays of length n + 2 of numbers in 0..3. 1
13, 103, 625, 3151, 14053, 58975, 242461, 989527, 4017157, 16245775, 65514541, 263652487, 1059392917, 4251920575, 17050729021, 68332056247, 273715645477, 1096024843375, 4387586157901, 17560804984807, 70274600998837 (list; graph; refs; listen; history; text; internal format)
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 09 2018: (Start)

G.f.: x*(13 + 12*x + 60*x^2 + 12*x^3 - 504*x^4 - 1584*x^5 - 1728*x^6) / ((1 - 3*x)*(1 - 4*x)).

a(n) = 4^(2+n) - 3^(2+n) for n>5.

(End)

EXAMPLE

Some solutions for n=4:

..5....0...-5....3....4....1....3...-3...-6....2....2....1...-5....1....0....2

.-4....2....2...-3...-5....1....1....3....3...-1....3....1....3....4....3....1

..2....0...-1....5....5...-3...-5....1....1....4...-5....1....0...-6...-3...-1

..3...-2....2...-6...-2....0....3...-5....1...-5....4...-1...-3....6....3....0

CROSSREFS

Column 3 of A228218.

Sequence in context: A085957 A119594 A066034 * A220734 A268991 A216179

Adjacent sequences:  A228210 A228211 A228212 * A228214 A228215 A228216

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 16 2013

STATUS

approved

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)