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A025089 a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n-k+1), where k = [n/2], s = (Lucas numbers). 0
0, 3, 4, 19, 32, 79, 127, 283, 459, 940, 1520, 2982, 4826, 9171, 14838, 27581, 44628, 81557, 131961, 237995, 385085, 687158, 1111844, 1966764, 3182292, 5588259, 9041992, 15780103, 25532744, 44323195, 71716435, 123920827, 200508111, 345062176, 558322328, 957403026 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
From Chai Wah Wu, Dec 24 2023: (Start)
a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - 2*a(n-5) - 3*a(n-6) + a(n-7) + a(n-8) for n > 8.
G.f.: x*(-4*x^5 - 2*x^4 + 7*x^3 + 6*x^2 + x + 3)/((x^2 + 1)*(-x^2 + x + 1)*(x^2 + x - 1)^2).
(End)
MATHEMATICA
a[n_]:=Sum[LucasL[i]LucasL[n-i+1], {i, Floor[n/2]}]; Array[a, 36] (* Stefano Spezia, Dec 24 2023 *)
CROSSREFS
Cf. A000204 (Lucas), A004526 ([n/2]).
Sequence in context: A212113 A196133 A330436 * A041989 A196198 A041561
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(1) inserted by Chai Wah Wu, Dec 24 2023
More terms from Stefano Spezia, Dec 24 2023
STATUS
approved

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Last modified April 16 00:45 EDT 2024. Contains 371696 sequences. (Running on oeis4.)