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A102591 a(n)=sum k=0..n, C(2n+1,2k)3^(n-k). 6
1, 6, 44, 328, 2448, 18272, 136384, 1017984, 7598336, 56714752, 423324672, 3159738368, 23584608256, 176037912576, 1313964867584, 9807567290368, 73204678852608, 546407161659392, 4078438577864704, 30441879976280064 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, sum{k=0..n, C(2n+1,2k)r^(n-k)} has g.f. (1-(r-1)x)/(1-2(r+1)+(r-1)^2x^2) and a(n)=((sqrt(r)-1)^(2n+1)+(sqrt(r)+1)^(2n+1))/(2sqrt(r)).

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (8,-4).

FORMULA

G.f.: (1-2x)/(1-8x+4x^2); a(n)=8a(n-1)-4a(n-2); a(n)=sqrt(3)(sqrt(3)-1)^(2n+1)/6+sqrt(3)(sqrt(3)+1)^(2n+1)/6.

a(n) = 2^n*A079935(n). - R. J. Mathar, Sep 20 2012

CROSSREFS

Cf. A066443, A102592, bisection of A080879 or A002605.

Sequence in context: A091163 A189800 A227665 * A114935 A115969 A082412

Adjacent sequences:  A102588 A102589 A102590 * A102592 A102593 A102594

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 22 2005

STATUS

approved

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Last modified September 22 13:53 EDT 2020. Contains 337289 sequences. (Running on oeis4.)