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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
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1860498, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
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
KEYWORD
nonn,frac,easy
EXTENSIONS
More terms from Vincenzo Librandi, Dec 27 2013
STATUS
approved