[seqfan] Re: Paraffin Numbers

[Simon Plouffe]

Hello,

  Most of the formulas for the paraffins where found a while ago
(1992). here :
http://arxiv.org/ftp/arxiv/papers/0911/0911.4975.pdf

see page 448 and forward there are dozen of related formulas
for paraffins using infinite products.

  Best regards,
  Simon Plouffe


Le 11/03/2012 10:24, Psychedelic Geometry a écrit :
> Hello:
>
> The following Mathematica code seems to generate sequence A006009: Number of
> paraffins.
>
> A006009[n_] := Sum[(i + 1)*Floor[(i + 1)^2/2], {i, 1, n}];
>
> And if this conjecture is correct then the Alkane (or paraffin) numbers
> l(7,n) should be:
>
> A005994[n_] := Sum[(i + 1)*Floor[(i + 1)^2/2], {i, 1, n}]/2 - Binomial[n +
> 3, 4];
>
>
>
> Does anybody knows how to prove o disprove these formulas?
>
>
> Best Regards, Enrique.
>
>
>
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