Revision History for A089106
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#9 by Alois P. Heinz at Sat Dec 09 11:08:42 EST 2017
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#8 by Robert G. Wilson v at Sat Dec 09 09:20:58 EST 2017
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#7 by Jean-François Alcover at Sat Dec 09 08:55:08 EST 2017
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#6 by Jean-François Alcover at Sat Dec 09 08:55:04 EST 2017
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| MATHEMATICA
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terms = 27; r = 10; f[z_] := -1/(1 - z - z^2);
W = (z/r)*Sum[MoebiusMu[d]*f[z^d]^(r/d), {d, Divisors[r]}]+ O[z]^(terms+1);
CoefficientList[W, z] // Rest (* Jean-François Alcover, Dec 09 2017, from Maple *)
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| STATUS
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approved
editing
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#5 by Russ Cox at Fri Mar 30 17:35:54 EDT 2012
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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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Discussion
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| Fri Mar 30
| 17:35
| OEIS Server: https://oeis.org/edit/global/173
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#4 by Russ Cox at Fri Mar 30 16:49:50 EDT 2012
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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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Discussion
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| Fri Mar 30
| 16:49
| OEIS Server: https://oeis.org/edit/global/110
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#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009
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| KEYWORD
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nonn,new
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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#2 by N. J. A. Sloane at Sat Jun 12 03:00:00 EDT 2004
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| NAME
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ConvolutedSign twisted convoluted convolved Fibonacci numbers. H_j^(10).
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| DATA
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0, 1, 7, 33, 145, 552, 1959, 6435, 20039, 59345, 168862, 463385, 1233082, 3191530, 8061718, 19919613, 48255611, 114812555, 268730241, 619603435, 1409012926, 3163562545, 7019590107, 15405769535, 33467218583, 72013318602, 153577843509
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| COMMENTS
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See Moree paper for precise definition and recurrences.
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| FORMULA
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G.f.: (z/10)[1/(1-z-z^2)^10+1/(1-z^2-z^4)^5-1/(1-z^5-z^10)^2-1/(1-z^10-z^20)].
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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(10, j), j=1..35);
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| KEYWORD
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nonn,new
nonn
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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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#1 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004
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| NAME
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Convoluted convolved Fibonacci numbers.
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| DATA
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0, 1, 7, 33, 145, 552, 1959, 6435, 20039, 59345, 168862
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| OFFSET
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1,3
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| COMMENTS
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See Moree paper for precise definition and recurrences.
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| LINKS
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P. Moree, <a href="http://arXiv.org/abs/math.CO/0311205">Convoluted convolved Fibonacci numbers</a>
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| KEYWORD
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nonn
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| AUTHOR
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njas, Dec 05 2003
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| STATUS
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approved
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