Exact formulas for integer sequences
Olivier Gerard
ogerard at ext.jussieu.fr
Wed Mar 24 02:19:16 CET 2004
From: Simon Plouffe <simon.plouffe at sympatico.ca>
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hello,
(this is old material from 1993),
I collected some of my notes about exact formulas for
integer sequences. They are somewhat usefull since it can be
used to compute the n'th term of a sequence.
it uses [ ] , { } and some constants like exp(1).
http://www.lacim.uqam.ca/%7Eplouffe/exact.htm
note : most of those formulas do not appear in the current On-line
Encyclopedia of integer sequences.
By the way, can anybody do this : Can we find an EXACT formula for
the n'th term of A001006 (Motzkin numbers), the only useful formula
we have is a recurrence but with the index that grows with n which
makes it difficult to compute for large n.
http://www.research.att.com/projects/OEIS?Anum=A001006 is
1,1,2,4,9,21,51,127,323,835,2188,5798, ... and it grows roughly like
3^n.
Simon Plouffe
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