A041955 Denominators of continued fraction convergents to sqrt(500).

1, 2, 3, 11, 25, 36, 61, 646, 707, 1353, 3413, 11592, 15005, 41602, 1845493, 3732588, 5578081, 20466831, 46511743, 66978574, 113490317, 1201881744, 1315372061, 2517253805, 6349879671, 21566892818, 27916772489, 77400437796, 3433536035513, 6944472508822

Offset

0,2

Links

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

Formula

G.f.: -(x^26 -2*x^25 +3*x^24 -11*x^23 +25*x^22 -36*x^21 +61*x^20 -646*x^19 +707*x^18 -1353*x^17 +3413*x^16 -11592*x^15 +15005*x^14 -41602*x^13 -15005*x^12 -11592*x^11 -3413*x^10 -1353*x^9 -707*x^8 -646*x^7 -61*x^6 -36*x^5 -25*x^4 -11*x^3 -3*x^2 -2*x -1)/(x^28 -1860498*x^14 +1). - Vincenzo Librandi, Dec 27 2013

a(n) = 1860498*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator[Convergents[Sqrt[500], 30]] (* or *) CoefficientList[Series[-(x^26 - 2 x^25 + 3 x^24 - 11 x^23 + 25 x^22 - 36 x^21 + 61 x^20 - 646 x^19 + 707 x^18 - 1353 x^17 + 3413 x^16 - 11592 x^15 + 15005 x^14 - 41602 x^13 - 15005 x^12 - 11592 x^11 - 3413 x^10 - 1353 x^9 - 707 x^8 - 646 x^7 - 61 x^6 - 36 x^5 - 25 x^4 - 11 x^3 - 3 x^2 - 2 x - 1)/(x^28 - 1860498 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 27 2013 *)

Prog

(Magma) I:=[1, 2, 3, 11, 25, 36, 61, 646, 707, 1353, 3413, 11592, 15005, 41602, 1845493, 3732588, 5578081, 20466831, 46511743, 66978574, 113490317, 1201881744, 1315372061, 2517253805, 6349879671, 21566892818, 27916772489, 77400437796]; [n le 28 select I[n] else 1860498*Self(n-14)-Self(n-28): n in [1..40]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A041954.

Sequence in context: A065849 A136402 A137811 * A239445 A157161 A041811

Adjacent sequences: A041952 A041953 A041954 * A041956 A041957 A041958

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 27 2013

Status

approved