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Search: id:A089093
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| A089093 |
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Convoluted convolved Fibonacci numbers G_j^(6). |
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+0
1
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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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 (mathar(AT)strw.leideuniv.nl), Nov 08 2008]
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LINKS
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P. Moree, Convoluted convolved Fibonacci numbers
Pieter Moree, The formal series Witt transform, Discr. Math. no. 295 vol. 1-3 (2005) 143-160. [From R. J. Mathar (mathar(AT)strw.leideuniv.nl), Nov 08 2008]
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FORMULA
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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)].
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MAPLE
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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);
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CROSSREFS
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Sequence in context: A114185 A085697 A121184 this_sequence A058234 A007688 A100774
Adjacent sequences: A089090 A089091 A089092 this_sequence A089094 A089095 A089096
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 05 2003
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EXTENSIONS
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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2004
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