A042032 Numerators of continued fraction convergents to sqrt(540).

23, 93, 395, 488, 5275, 5763, 28327, 119071, 5505593, 22141443, 94071365, 116212808, 1256199445, 1372412253, 6745848457, 28355806081, 1311112928183, 5272807518813, 22402343003435, 27675150522248, 299153848225915, 326828998748163, 1606469843218567

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,238142,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^15 -23*x^14 +93*x^13 -395*x^12 +488*x^11 -5275*x^10 +5763*x^9 -28327*x^8 -119071*x^7 -28327*x^6 -5763*x^5 -5275*x^4 -488*x^3 -395*x^2 -93*x -23) / ((x^8 -488*x^4 +1)*(x^8 +488*x^4 +1)). - Colin Barker, Nov 29 2013

a(n) = 238142*a(n-8) - a(n-16). - Wesley Ivan Hurt, Sep 05 2022

Mathematica

Numerator[Convergents[Sqrt[540], 30]]  (* Vincenzo Librandi, Nov 14 2013 *)

Crossrefs

Cf. A042033, A040516.

Sequence in context: A317371 A244632 A042030 * A257976 A183011 A158544

Adjacent sequences: A042029 A042030 A042031 * A042033 A042034 A042035

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 29 2013

Status

approved