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A164267 A Fibonacci convolution. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A248114 A330227

Adjacent sequences:  A164264 A164265 A164266 * A164268 A164269 A164270

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 11 2009

STATUS

approved

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Last modified January 19 18:13 EST 2020. Contains 331051 sequences. (Running on oeis4.)