Need some help from Fibonacci experts...
Ron Knott
ron at ronknott.com
Sun Jul 31 00:04:38 CEST 2005
Also, Mathematica has a comprehensive collection of transformations of Fibonacci Numbers implemented by Stanley Rabinowitz I believe, based on his papers (the first is in Applications of Fibonaci Numbers vol 6, pages 389-408) on how to compare an amazingly large family of Fibonacci formula and verify their correctness. A subsequent paper deals with second order linear forms and a final oone on third order. I know he was asking (in 1996) for volunteers to implement the algorithms in Maple but they do not appear to be there yet (unless someone knows where). Virtually any of the known identities and many suggested ones involving sums, products, powers of Fib numbers, with indices of a linear form are covered in his methods.
Ron Knott
>> Thank you very much for that !!! Now, is there somewhere available a kind
>> of encyclopedy of basic algebraic "primitive" ogf (in order to recognize
>> factors of the denominator) ?
>
>Heh, such a database would be the only part missing if you want to
>build a program that does automatic simplification (and recognition
>like superseeker, because you can feed it sequences instead of
>expressions).
>
>I think one could just take all OEIS sequences with rational ogf.
>To recognize them, either parse %F lines or use ggf() but this catches
>false positives because some sequences are too short. I could mail you
>my list of ggf() positives, then you just weed out those not having a
>meaningful %F with rat.g.f., and there is your database.
>But keep in mind that offsets can go wrong, i.e., g.f.s may have
>factors 1,x,x^2,x^3...
>
>Implementation issues are not relevant to the list, so please mail.
>
>
>ralf
>
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