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This part of the Auto-generate project is concerned with recognizing the type/definition of the sequence and then, in particular, extracting the coefficients. Please see the talk page for the discussion.

Aim and scope

We need to know

  • whether a given sequence is of "allowed type" ("currently": linear recurrence with constant coefficients)
  • whether the data (DATA & other: link to index/Rec#order.. & signature; ...) is sufficient to compute anything
  • whether it is of some particular sub-class:
    • polynomial : yields particularly simple formulae & programs
    • large data / coefficients: in computations of data, care must be taken to avoid corrupt results. Use qualitative and/or quantitative indicators for this. Fix limits on index, size of a(n), add consistency checks (a(n) mod p or similar) to detect unexpected errors. Report such errors.
    • linear recurrence of low orders: special formulae & methods exist for 1st, 2nd,... order linear recurrences, etc.
  • what (other) consistency checks should be added: compare information from scan of NAME, "hand made" FORMULAs, PROGRAMs...


(detailed considerations concerning the above points)

How the type of a sequence is determined

  • use ggf on DATA ?
  • use LINKS to /index/Rec#... & signature ?
  • scan NAME or FORMULA for simple patterns ?

Consistency checks

Compare the result obtained from the various sources above.


Here go the scripts. We split up nontrivial parts (functions) for easier editing & documentation in separate subsections when this seems useful.