A042457 Denominators of continued fraction convergents to sqrt(756).

1, 2, 109, 220, 11989, 24198, 1318681, 2661560, 145042921, 292747402, 15953402629, 32199552660, 1754729246269, 3541658045198, 193004263686961, 389550185419120, 21228714276319441, 42846978738058002, 2334965566131451549, 4712778111000961100

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,110,0,-1).

Formula

G.f.: -(x^2-2*x-1) / (x^4-110*x^2+1). - Colin Barker, Dec 14 2013

Mathematica

Denominator[Convergents[Sqrt[756], 30]] (* Harvey P. Dale, Aug 17 2012 *)
CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 110 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 22 2014 *)

Prog

(Magma) I:=[1, 2, 109, 220]; [n le 4 select I[n] else 110*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 22 2014

Crossrefs

Cf. A042456, A040728.

Sequence in context: A247098 A245056 A023281 * A062656 A173372 A323250

Adjacent sequences: A042454 A042455 A042456 * A042458 A042459 A042460

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Dec 14 2013

Status

approved