A089113 Convoluted convolved Fibonacci numbers G_7^(r).

13, 34, 77, 146, 259, 418, 654, 967, 1396, 1946, 2665, 3555, 4683, 6048, 7728, 9729, 12141, 14966, 18319, 22198, 26732, 31928, 37930, 44740, 52533, 61306, 71251, 82376, 94891, 108798, 124344, 141525, 160608, 181602, 204795, 230189, 258115

Offset

1,1

Links

Table of n, a(n) for n=1..37.

P. Moree, Convoluted convolved Fibonacci numbers

Formula

Empirical g.f.: -x*(2*x^14 -4*x^13 -2*x^12 +6*x^11 +2*x^10 -5*x^9 -8*x^8 +10*x^7 +12*x^6 -6*x^5 -5*x^4 +3*x^3 +4*x^2 -8*x -13) / ((x -1)^6 * (x +1)^3 * (x^2 -x +1) * (x^2 +x +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(m(r, 7), r=1..65);

Mathematica

terms = 40; f[z_] = 1/(1-z-z^2); m[r_, j_] := SeriesCoefficient[(1/r)*z* DivisorSum[r, MoebiusMu[#]*f[z^#]^(r/#)&], {z, 0, j}]; Table[m[r, 7], {r, 1, terms}] (* Jean-François Alcover, Apr 01 2018 *)

Crossrefs

Sequence in context: A180673 A081752 A069484 * A067430 A214729 A280322

Adjacent sequences: A089110 A089111 A089112 * A089114 A089115 A089116

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved