A144830 Numerators of the convergents to x = 1/(x^4+1).

1, 1, 16, 83521, 493639046268679584001

Offset

0,3

Comments

These numbers are quartics. The recursion provides a method of solving the quintic x^5 + x - 1. In general, extending this notion, we can use the recursion x = 1/(x^(n-1)+1) to find a solution for n-th degree equations of the form x^n+x-1=0.

Links

Table of n, a(n) for n=0..4.

Prog

(PARI) x=0; for(j=1, 7, x=1/(x^4+1); print1((numerator(x))", "))

Crossrefs

Sequence in context: A193135 A368326 A308507 * A278289 A298202 A364777

Adjacent sequences: A144827 A144828 A144829 * A144831 A144832 A144833

Keyword

frac,nonn

Author

Cino Hilliard, Sep 21 2008

Status

approved