A025096 - OEIS

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A025096

a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A000032, t = A023533.

0, 0, 1, 3, 4, 0, 0, 0, 1, 3, 4, 7, 11, 18, 29, 47, 76, 0, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2208, 3574, 5782, 9356, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39604, 64082, 103686, 167768, 271454

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 2..5000

MATHEMATICA

A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3]!= n, 0, 1];

A025096[n_]:= A025096[n]= Sum[LucasL[j]*A023533[n-j+1], {j, Floor[n/2]}];

Table[A025096[n], {n, 2, 100}] (* G. C. Greubel, Sep 08 2022 *)

PROG

(Magma)

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;