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A093129 Binomial transform of Fib(2n-1) (A001519). 10
1, 2, 5, 15, 50, 175, 625, 2250, 8125, 29375, 106250, 384375, 1390625, 5031250, 18203125, 65859375, 238281250, 862109375, 3119140625, 11285156250, 40830078125, 147724609375, 534472656250, 1933740234375, 6996337890625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (5,-5).

FORMULA

G.f.: (1-3x)/(1-5x+5x^2);

a(n) = (5-sqrt(5))((5+sqrt(5))/2)^n/10 + (5+sqrt(5))((5-sqrt(5))/2)^n/10;

a(n) = A093123(n)/2^n.

a(n) = A020876(n-1). - R. J. Mathar, Sep 05 2008

a(n) = A030191(n)-3*A030191(n-1). - R. J. Mathar, Jun 29 2012

MAPLE

a:= n-> (<<0|1>, <-5|5>>^n. <<1, 2>>)[1, 1]:

seq(a(n), n=0..30);  # Alois P. Heinz, Aug 29 2015

PROG

(Sage) [lucas_number2(n, 5, 5) for n in xrange(-1, 25)] # Zerinvary Lajos, Jul 08 2008

CROSSREFS

Cf. A000045.

Sequence in context: A149946 A149947 A149948 * A020876 A228343 A149949

Adjacent sequences:  A093126 A093127 A093128 * A093130 A093131 A093132

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 23 2004

STATUS

approved

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Last modified January 17 10:30 EST 2019. Contains 319218 sequences. (Running on oeis4.)