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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Index entries for linear recurrences with constant coefficients, signature (1,3,-2,0,-2,-3,1,1).

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

Adjacent sequences: A025086 A025087 A025088 * A025090 A025091 A025092

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

a(1) inserted by Chai Wah Wu, Dec 24 2023

More terms from Stefano Spezia, Dec 24 2023

Status

approved