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A033891 Fibonacci(4n+3). 15
2, 13, 89, 610, 4181, 28657, 196418, 1346269, 9227465, 63245986, 433494437, 2971215073, 20365011074, 139583862445, 956722026041, 6557470319842, 44945570212853, 308061521170129, 2111485077978050 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..18.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (7,-1).

FORMULA

a(n) = 7*a(n-1)-a(n-2). - Floor van Lamoen, Dec 10 2001

a(n) = (7/2-(3/2)*sqrt(5))^n-(2/5)*(7/2-(3/2)*sqrt(5))^n*sqrt(5)+(2/5)*sqrt(5)*(7/2+(3/2) *sqrt(5))^n+(7/2+(3/2)*sqrt(5))^n, with n>=0. - Paolo P. Lava, Jun 25 2008

G.f.: (2-x)/(1-7*x+x^2). - Philippe Deléham, Nov 17 2008

a(n) = Fibonacci(2*n+2)^2 + Fibonacci(2*n+1)^2. - Gary Detlefs, Oct 12 2011

a(n) = 2*A004187(n+1)-A004187(n). - R. J. Mathar, Nov 26 2011

a(n) = A004187(n+1) + A049685(n). - Yuriy Sibirmovsky, Sep 15 2016

MATHEMATICA

Table[Fibonacci[4*n+3], {n, 0, 14}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2008 *)

LinearRecurrence[{7, -1}, {2, 13}, 31] (* or *) CoefficientList[Series[ (2-x)/(1-7x+x^2), {x, 0, 30}], x] (* Harvey P. Dale, May 03 2011 *)

PROG

(MAGMA) [Fibonacci(4*n +3): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011

(PARI) a(n)=fibonacci(4*n+3) \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

a(n) = A167816(4*n+3). - Reinhard Zumkeller, Nov 13 2009

Cf. A004187, A049685.

Sequence in context: A092849 A106938 A106937 * A172968 A126035 A074617

Adjacent sequences:  A033888 A033889 A033890 * A033892 A033893 A033894

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 26 01:26 EDT 2017. Contains 287073 sequences.