

A099924


Selfconvolution 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
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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 selfconvolution of the kFibonacci sequence, Notes on Number Theory and Discrete Mathematics (2020) Vol. 26, No. 3, 96106.
Tamás Szakács, Convolution of second order linear recursive sequences. II. Commun. Math. 25, No. 2, 137148 (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(nk).
G.f.: (2x)^2/(1xx^2)^2, corrected Aug 23 2022
a(n) = 2*a(n1) + a(n2)  2*a(n3)  a(n4), 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[nk], {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



