[seqfan] nonlinear relations and doubling formulas for a sequence (new, autoverification)

Georgi Guninski guninski at guninski.com
Wed Sep 1 15:05:10 CEST 2010

```using stefun [1] i looked for nonlinear relations and doubling formulas in one sequence using at least 900 terms from a sequence. found about 2000 potential relations in a subset of oeis (10K) , the
number of really wrong relations is expected to be low (not counting tautologies like "twin primes differ by 2").

main new features:
0. automatic verification of the found relation to max available terms
1. easy conversion relation <-> symbolic expression allowing symbolic solving
2. HTML pretty printing
3. trivial conversion to \TeX using sage.

a typical entry is:
--------
Name : Number of binary partitions: number of partitions of 2n into powers of 2.
__: 1, 2, 4, 6, 10, 14, 20, 26

Comments : Possible relation vrfd to 9984 (of ~9984)
Formula: -a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) + 2*a(n - 1)^2 + 2*a(n - 1)*a(n + 1) - 5*a(n - 1)*a(n) - a(n + 1)*a(n) + 2*a(n)^2
--------

searchable interface:
http://stefan.guninski.com/cgi/oeis-base1.cgi?q=%25N

the database in OEIS format:
http://stefan.guninski.com/seq/base1

the progam stefun (needs sage) is availabe at:
[1] http://www.guninski.com/nmbrz/stefuni-pub.sage

```