A042061 Denominators of continued fraction convergents to sqrt(554).

1, 1, 2, 13, 54, 67, 121, 551, 3427, 3978, 7405, 344608, 352013, 696621, 4531739, 18823577, 23355316, 42178893, 192070888, 1194604221, 1386675109, 2581279330, 120125524289, 122706803619, 242832327908, 1579700771067, 6561635412176, 8141336183243

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,348586,0,0,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^20 -x^19 +2*x^18 -13*x^17 +54*x^16 -67*x^15 +121*x^14 -551*x^13 +3427*x^12 -3978*x^11 +7405*x^10 +3978*x^9 +3427*x^8 +551*x^7 +121*x^6 +67*x^5 +54*x^4 +13*x^3 +2*x^2 +x +1) / (x^22 +348586*x^11 -1). - Colin Barker, Nov 30 2013

Mathematica

Denominator[Convergents[Sqrt[554], 30]] (* Harvey P. Dale, Jan 27 2013 *)
CoefficientList[Series[-(x^20 - x^19 + 2 x^18 - 13 x^17 + 54 x^16 - 67 x^15 + 121 x^14 - 551 x^13 + 3427 x^12 - 3978 x^11 + 7405 x^10 + 3978 x^9 + 3427 x^8 + 551 x^7 + 121 x^6 + 67 x^5 + 54 x^4 + 13 x^3 + 2 x^2 + x + 1)/(x^22 + 348586 x^11 - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 13 2014 *)

Crossrefs

Cf. A042060, A040530.

Sequence in context: A177077 A144235 A180041 * A229736 A187560 A338818

Adjacent sequences: A042058 A042059 A042060 * A042062 A042063 A042064

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 30 2013

Status

approved