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A099924
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Self-convolution of Lucas numbers.
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3
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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
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0,1
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 57.
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 0..4767
É. Czabarka, R. Flórez, 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.
Index entries for linear recurrences with constant coefficients, signature (2, 1, -2, -1).
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FORMULA
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a(n) = (n+1)*L(n) + 2F(n+1) = Sum_{k=0..n} L(k)*L(n-k).
G.f.: (4-4x-x^2)/(1-x-x^2)^2.
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
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Nov 01 2004
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STATUS
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approved
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