A025089 - OEIS

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

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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