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A089093 Convoluted convolved Fibonacci numbers G_j^(6). 0
0, 1, 4, 16, 51, 154, 418, 1098, 2726, 6570, 15308, 34839, 77412, 168882, 361896, 764097, 1590938, 3272640, 6656426, 13403600, 26739028, 52892435, 103806344, 202263470, 391460137, 752923563, 1439737364, 2738144031, 5181025837 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The 6th Witt transform of A000045 [Moree]. The 2nd to 5th Witt transforms are (essentially, adding leading zeros) in A089089, A089116, A089117, A089092. [From R. J. Mathar, Nov 08 2008]

LINKS

Table of n, a(n) for n=1..29.

P. Moree, Convoluted convolved Fibonacci numbers

Pieter Moree, The formal series Witt transform, Discr. Math. no. 295 vol. 1-3 (2005) 143-160.

FORMULA

G.f.: (z/6)[1/(1-z-z^2)^6-1/(1-z^2-z^4)^3-1/(1-z^3-z^6)^2+1/(1-z^6-z^12)].

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(6, j), j=1..40);

MATHEMATICA

f[k_] = 1/(1 - z^k - z^(2k))^(6/k); (1/6) (f[1] - f[2] - f[3] + f[6]) + O[z]^30 // CoefficientList[#, z]& (* Jean-Fran├žois Alcover, Mar 24 2018 *)

CROSSREFS

Sequence in context: A323932 A121184 A203840 * A316321 A058234 A188125

Adjacent sequences:  A089090 A089091 A089092 * A089094 A089095 A089096

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 05 2003

EXTENSIONS

Edited by Emeric Deutsch, Mar 06 2004

STATUS

approved

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Last modified August 4 16:10 EDT 2021. Contains 346447 sequences. (Running on oeis4.)