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A041955 Denominators of continued fraction convergents to sqrt(500). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 24 16:16 EDT 2019. Contains 322430 sequences. (Running on oeis4.)