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A099924 Self-convolution of Lucas numbers. 3
4, 4, 13, 22, 45, 82, 152, 274, 491, 870, 1531, 2676, 4652, 8048, 13865, 23798, 40713, 69446, 118144, 200510, 339559, 573894, 968183, 1630632, 2742100, 4604572, 7721797, 12933334, 21637221, 36159610, 60367976, 100687786 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 57.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..4767

É. Czabarka, R. Flórez, and L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.

Sergio Falcon, Half self-convolution of the k-Fibonacci sequence, Notes on Number Theory and Discrete Mathematics (2020) Vol. 26, No. 3, 96-106.

Tamás Szakács, Convolution of second order linear recursive sequences. II. Commun. Math. 25, No. 2, 137-148 (2017). See remark 4.

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

FORMULA

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

G.f.: (2-x)^2/(1-x-x^2)^2, corrected Aug 23 2022

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4), a(0)=4, a(1)=4, a(2)=13, a(3)=22. - Harvey P. Dale, Mar 06 2012

a(n) = 2*A099920(n+1)-A099920(n). - R. J. Mathar, Aug 23 2022

MATHEMATICA

Table[Sum[LucasL[k]LucasL[n-k], {k, 0, n}], {n, 0, 40}] (* or *) LinearRecurrence[ {2, 1, -2, -1}, {4, 4, 13, 22}, 40] (* Harvey P. Dale, Mar 06 2012 *)

CROSSREFS

Cf. A001629, A000032. Bisection: A203573 (even), 2*A203574 (odd).

Sequence in context: A214779 A323920 A005301 * A147824 A019081 A219454

Adjacent sequences: A099921 A099922 A099923 * A099925 A099926 A099927

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Nov 01 2004

STATUS

approved

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Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)