A095122 Fib(n)(2Fib(n)-1).

0, 1, 1, 6, 15, 45, 120, 325, 861, 2278, 5995, 15753, 41328, 108345, 283881, 743590, 1947351, 5099221, 13351528, 34957341, 91523685, 239618886, 627341331, 1642418641, 4299936480, 11257426225, 29472399505, 77159865030, 202007345631

Offset

0,4

Comments

mod(A095122(n),2)=mod(Fib(n),2)=A011655(n)

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1).

Formula

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

a(n)=2(Fib(2n-1)+Fib(2n+1))/5-Fib(n)+4(-1)^n/5;

a(n)=2L(2n)/5-Fib(n)+4(-1)^n/5;

a(n)=2*A000032(2n)/5-A000045(n)+4(-1)^n/5.

a(0)=0, a(1)=1, a(2)=1, a(3)=6, a(4)=15, a(n)=3*a(n-1)+a(n-2)- 5*a(n-3)- a(n-4)+a(n-5) [From Harvey P. Dale, Jan 14 2012]

Mathematica

#(2#-1)&/@Fibonacci[Range[0, 30]] (* or *) LinearRecurrence[{3, 1, -5, -1, 1}, {0, 1, 1, 6, 15}, 30] (* Harvey P. Dale, Jan 14 2012 *)

Crossrefs

Sequence in context: A117961 A327769 A318482 * A215917 A082637 A244023

Adjacent sequences: A095119 A095120 A095121 * A095123 A095124 A095125

Keyword

easy,nonn

Author

Paul Barry, May 29 2004

Status

approved