A049679 a(n) = (F(8*n+7)+F(8*n+5))/3, where F=A000045 (the Fibonacci sequence).

6, 281, 13201, 620166, 29134601, 1368706081, 64300051206, 3020733700601, 141910183877041, 6666757908520326, 313195711516578281, 14713531683370658881, 691222793406904389126, 32472757758441135630041, 1525528391853326470222801, 71667361659347902964841606

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..500

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (47,-1).

Formula

From Philippe Deléham, Nov 18 2008: (Start)

a(n) = 47*a(n-1) - a(n-2), a(0)=6, a(1)=281.

G.f.: (6-x)/(1-47*x+x^2). (End)

a(n) = (((5+3*sqrt(5))*(2/(47+21*sqrt(5)))^n + (1/2*(47+21*sqrt(5)))^n*(1885+843*sqrt(5))))/(315+141*sqrt(5)). - Colin Barker, May 05 2016

Mathematica

LinearRecurrence[{47, -1}, {6, 281}, 20] (* Harvey P. Dale, Dec 14 2014 *)
Table[(Fibonacci[8*n+7]+Fibonacci[8*n+5])/3, {n, 0, 30}] (* G. C. Greubel, Dec 02 2017 *)

Prog

(PARI) Vec((6-x)/(1-47*x+x^2) + O(x^20)) \\ Colin Barker, May 05 2016
(Magma) [(Fibonacci(8*n+7) + Fibonacci(8*n+5))/3: n in [0..30]]; // G. C. Greubel, Dec 02 2017
(PARI) for(n=0, 30, print1((fibonacci(8*n+7) + fibonacci(8*n+5))/3, ", ")) \\ G. C. Greubel, Dec 02 2017

Crossrefs

Sequence in context: A342983 A199093 A163015 * A201139 A172660 A203051

Adjacent sequences: A049676 A049677 A049678 * A049680 A049681 A049682

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Corrected and extended by T. D. Noe, Nov 07 2006

Status

approved