[seqfan] Re: "Start a sequence at the earliest reasonable point, but no earlier."

Richard Mathar mathar at strw.leidenuniv.nl
Thu Jul 29 16:10:05 CEST 2010


http://list.seqfan.eu/pipermail/seqfan/2010-July/005448.html spake

df> In the OEIS, the figurate numbers sequences authored by Neil Sloane
df> typically start at n = 0 giving 0 followed by n = 1 giving 1, while
df> the GLOBALLY centered figurate numbers start at n = 0 giving 1 for the
df> mandatory central dot.

Many of these sequences have simple polynomial representations. If one
of the factors is a 1-st order polynomial [example (3+n)*(n^3-4*n^2+10*n-3) ]
it is generally preferable to re-number this by the shift 3+n -> n which
changes the offset and maps the 1-st order polynomial to n.
Generally this normalizes the polynomial sequences to a(0)=0 by convention,
not referring to counts of some sort.
(It's in the bible: Am Anfang war die Welt wuest und leer, therefore a(0)=0 :-).

RJM




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