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A087124 a(n) = Fibonacci(n) + Fibonacci(2n+1). 3
1, 3, 6, 15, 37, 94, 241, 623, 1618, 4215, 11001, 28746, 75169, 196651, 514606, 1346879, 3525565, 9229062, 24160401, 63250167, 165586906, 433505383, 1134920881, 2971243730, 7778788417, 20365086099, 53316412566, 139584058863 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A087123.

For n>=1, a(n) is the coefficient of x in the reduction by x^2->x+1 of the polynomial 1+x^n+x^(2n+1).  For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232. - Clark Kimberling, Jul 01 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1).

FORMULA

G.f.: (1-2*x)*(1+x-x^2)/((1-3*x+x^2)*(1-x-x^2)). - Colin Barker, Mar 12 2012

MATHEMATICA

CoefficientList[Series[(1-2*x)*(1+x-x^2)/((1-3*x+x^2)*(1-x-x^2)), {x, 0, 1001}], x] (* Vincenzo Librandi, Mar 13 2012 *)

PROG

(MAGMA) [Fibonacci(n)+Fibonacci(2*n+1): n in [0..40]]; // Vincenzo Librandi, Mar 13 2012

(PARI) a(n)=fibonacci(n)+fibonacci(2*n+1) \\ Charles R Greathouse IV, Mar 13 2012

CROSSREFS

Cf. A000045.

Sequence in context: A058534 A063778 A279374 * A086326 A098701 A218777

Adjacent sequences:  A087121 A087122 A087123 * A087125 A087126 A087127

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 15 2003

STATUS

approved

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Last modified December 12 03:27 EST 2018. Contains 318052 sequences. (Running on oeis4.)