A121364 Convolution of A066983 with the double Fibonacci sequence A103609.

0, 0, 1, 2, 3, 6, 10, 18, 29, 50, 81, 136, 220, 364, 589, 966, 1563, 2550, 4126, 6710, 10857, 17622, 28513, 46224, 74792, 121160, 196041, 317434, 513619, 831430, 1345282, 2177322, 3522981, 5701290, 9224881, 14927768, 24153636, 39083988, 63239221, 102327390

Offset

1,4

Comments

The convolution of 1,0,1,1,1,3,3,7,9,17,25,... (A066983 with 1,0 added to the front) with "A double Fibonacci sequence" (A103609) is the Fibonacci sequence (A000045), with an extra initial 0.

Links

Table of n, a(n) for n=1..40.

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,0,-1,-1).

Formula

a(n) = F(n) - D(n+1), where F is the Fibonacci sequence (A000045) and D is "A double Fibonacci sequence" (A103609).

G.f.: -x^3*(x^2-x-1) / ((x^2+x-1)*(x^4+x^2-1)). - Colin Barker, Oct 13 2014

Example

a(7)=10 because F(7)=13 and D(8)=3 and a(7)=F(7)-D(8).

Prog

(PARI) concat([0, 0], Vec(-x^3*(x^2-x-1)/((x^2+x-1)*(x^4+x^2-1)) + O(x^100))) \\ Colin Barker, Oct 13 2014

Crossrefs

Cf. A066983, A103609, A000045.

Sequence in context: A065441 A075531 A066067 * A347787 A215006 A364463

Adjacent sequences: A121361 A121362 A121363 * A121365 A121366 A121367

Keyword

nonn,easy

Author

Graeme McRae, Jul 23 2006

Extensions

More terms from Colin Barker, Oct 13 2014

Status

approved