A164267 A Fibonacci convolution.

0, 1, 2, 7, 16, 46, 114, 309, 792, 2101, 5456, 14356, 37468, 98281, 256998, 673323, 1761984, 4614226, 12078110, 31624285, 82787980, 216750601, 567446112, 1485616392, 3889356696, 10182528721, 26658108074, 69791991919, 182717549872

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

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

a(n) = Sum_{k=0..n} (-1)^k*F(k+1)*F(2(n-k)).

a(n) = Sum_{k=0..n} C(n,k)*F(k+1)*(1-(-1)^(n-k))/2.

a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) + a(n-4).

a(n) = (A122367(n) - A039834(n-1))/2. - R. J. Mathar, Aug 17 2009

Mathematica

LinearRecurrence[{2, 3, -4, 1}, {0, 1, 2, 7}, 30] (* Harvey P. Dale, Jul 12 2011 *)
CoefficientList[Series[x / ((1 + x - x^2) (1 - 3 x + x^2)), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 13 2017 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(x/((1+x-x^2)*(1-3*x+x^2)))) \\ G. C. Greubel, Sep 12 2017
(Magma) I:=[0, 1, 2, 7]; [n le 4 select I[n] else 2*Self(n-1)+3*Self(n-2)-4*Self(n-3)+Self(n-4): n in [1..30]]; // Vincenzo Librandi, Sep 13 2017

Crossrefs

Sequence in context: A309561 A026571 A100099 * A184352 A368421 A248114

Adjacent sequences: A164264 A164265 A164266 * A164268 A164269 A164270

Keyword

easy,nonn

Author

Paul Barry, Aug 11 2009

Status

approved