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A099842 Expansion of (1-x)/(1+6x-3x^2). 4
1, -7, 45, -291, 1881, -12159, 78597, -508059, 3284145, -21229047, 137226717, -887047443, 5733964809, -37064931183, 239591481525, -1548743682699, 10011236540769, -64713650292711, 418315611378573, -2704034619149571, 17479154549033145, -112987031151647583 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A transformation of x/(1-2x-2x^2).

The g.f. is the transform of the g.f. of A002605 under the mapping G(x)-> (-1/(1+x))G((x-1)/(x+1)). In general this mapping transforms x/(1-kx-kx^2) into (1-x)/(1+2(k+1)x-(2k-1)x^2).

For n >= 1, |a(n)| equals the numbers of words of length n-1 on alphabet {0,1,...,6} containing no subwords 00, 11, 22, 33. - Milan Janjic, Jan 31 2015

LINKS

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (-6,3).

FORMULA

G.f.: (1-x)/(1+6*x-3*x^2).

a(n) = (1/2 - sqrt(3)/3)*(-3 + 2*sqrt(3))^n + (1/2 + sqrt(3)/3)*(-3 - 2*sqrt(3))^n.

a(n) = (-1)^n*Sum_{k=0..n} binomial(n, k)(-1)^(n-k)*A002605(2k+2)/2.

CROSSREFS

Sequence in context: A230760 A198629 A190973 * A287811 A115194 A062274

Adjacent sequences:  A099839 A099840 A099841 * A099843 A099844 A099845

KEYWORD

easy,sign,changed

AUTHOR

Paul Barry, Oct 27 2004

STATUS

approved

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)