[seqfan] Re: The Fibonomial Triangle

Richard Mathar mathar at strw.leidenuniv.nl
Mon Dec 6 15:07:04 CET 2010


rkg> ....
rkg>           How much of the following is known to those
rkg> who well know it?  I haven't yet been able to consult
rkg> Knuth, vol.1, p.85, so it may be there.  Or in Duke
rkg> Math J 29(1962) page numbers need correcting in some?
rkg> of [A000012, A000045, A007598], A056570--4, A056585--7.
rkg> The characteristic polynomials for these sequences are
rkg>                              x - 1
rkg>                           x^2 - x - 1
rkg> ...
rkg> which (it is known by some) factor into
rkg>                             x-1
rkg>                           x^2-x-1
rkg>                       (x+1)(x^2-3x+1)
rkg> ...

The factorization is basically a comment in A055870. The list of references
there is indeed small. So everybody with some additional references is welcome
to extend the list. There may be some more information in the Carlitz paper,

L. Carlitz, <a href="http://dx.doi.org/10.1215/S0012-7094-62-02953-8">Generating functions for powers of certain sequences of numbers</a>, Duke Math. J. 29 (4) (1962) 521-537

but I haven't tried to get access to the full paper.

Richard Mathar

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