A089111 Convoluted convolved Fibonacci numbers G_6^(r).

8, 19, 37, 64, 102, 154, 222, 309, 418, 552, 715, 910, 1141, 1412, 1727, 2091, 2508, 2983, 3521, 4127, 4807, 5566, 6410, 7345, 8377, 9513, 10759, 12122, 13609, 15227, 16984, 18887, 20944, 23163, 25552, 28120, 30875, 33826, 36982, 40352, 43946

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

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

Formula

Empirical g.f.: -x*(2*x^8-8*x^7+12*x^6-7*x^5-2*x^3+9*x^2-13*x+8) / ((x-1)^5*(x^4+x^3+x^2+x+1)). - 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(m(r, 6), r=1..65);

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[m[r, 6], {r, 1, 41}] (* Jean-François Alcover, Mar 25 2018, translated from Maple *)

Crossrefs

Sequence in context: A158916 A045557 A289877 * A127873 A192975 A156198

Adjacent sequences: A089108 A089109 A089110 * A089112 A089113 A089114

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved