A089110 Sign twisted convoluted convolved Fibonacci numbers H_5^(r).

5, 11, 17, 25, 38, 54, 70, 89, 115, 145, 175, 209, 252, 300, 348, 401, 465, 535, 605, 681, 770, 866, 962, 1065, 1183, 1309, 1435, 1569, 1720, 1880, 2040, 2209, 2397, 2595, 2793, 3001, 3230, 3470, 3710, 3961, 4235, 4521, 4807, 5105, 5428, 5764, 6100, 6449

Offset

1,1

Links

Table of n, a(n) for n=1..48.

P. Moree, Convoluted convolved Fibonacci numbers, arXiv:math/0311205 [math.CO], 2003.

Pieter Moree, Convoluted Convolved Fibonacci Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.

Formula

Empirical g.f.: -x*(x^7-4*x^6+8*x^5-12*x^4+15*x^3-13*x^2+9*x-5) / ((x-1)^4*(x^2+1)^2). - Colin Barker, Jul 31 2013

Maple

with(numtheory): f := z->-1/(1-z-z^2): m := proc(r, j) d := divisors(r): W := (1/r)*z*sum(mobius(d[i])*f(z^d[i])^(r/d[i]), i=1..nops(d)): Wser := simplify(series(W, z=0, 80)): coeff(Wser, z^j) end: seq((-1)^r*m(r, 5), r=1..60);

Mathematica

f[z_] = -1/(1 - z - z^2);
m[r_, j_] := (1/r)*z*DivisorSum[r, MoebiusMu[#]*f[z^#]^(r/#)&] // SeriesCoefficient[#, {z, 0, j}]&;
Table[(-1)^r*m[r, 5], {r, 1, 60}] (* Jean-François Alcover, Mar 27 2018 *)

Crossrefs

Sequence in context: A369274 A246296 A368874 * A023489 A268307 A108294

Adjacent sequences: A089107 A089108 A089109 * A089111 A089112 A089113

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved