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
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
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Nov 01 2004
STATUS
approved