A041915 Denominators of continued fraction convergents to sqrt(479).

1, 1, 8, 9, 35, 79, 1694, 3467, 12095, 15562, 121029, 136591, 5857851, 5994442, 47818945, 53813387, 209259106, 472331599, 10128222685, 20728776969, 72314553592, 93043330561, 723617867519, 816661198080, 35023388186879, 35840049384959

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, 0, 5978880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^22 -x^21 +8*x^20 -9*x^19 +35*x^18 -79*x^17 +1694*x^16 -3467*x^15 +12095*x^14 -15562*x^13 +121029*x^12 -136591*x^11 -121029*x^10 -15562*x^9 -12095*x^8 -3467*x^7 -1694*x^6 -79*x^5 -35*x^4 -9*x^3 -8*x^2 -x -1)/(x^24 -5978880*x^12 +1). - Vincenzo Librandi, Dec 27 2013

a(n) = 5978880*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator[Convergents[Sqrt[479], 30]] (* or *) CoefficientList[Series[-(x^22 - x^21 + 8 x^20 - 9 x^19 + 35 x^18 - 79 x^17 + 1694 x^16 - 3467 x^15 + 12095 x^14 - 15562 x^13 + 121029 x^12 - 136591 x^11 - 121029 x^10 - 15562 x^9 - 12095 x^8 - 3467 x^7 - 1694 x^6 - 79 x^5 - 35 x^4 - 9 x^3 - 8 x^2 - x - 1)/(x^24 - 5978880 x^12 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 27 2013 *)

Prog

(Magma) I:=[1, 1, 8, 9, 35, 79, 1694, 3467, 12095, 15562, 121029, 136591, 5857851, 5994442, 47818945, 53813387, 209259106, 472331599, 10128222685, 20728776969, 72314553592, 93043330561, 723617867519, 816661198080]; [n le 24 select I[n] else 5978880*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A041914.

Sequence in context: A050771 A120776 A041136 * A036764 A129548 A322797

Adjacent sequences: A041912 A041913 A041914 * A041916 A041917 A041918

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 27 2013

Status

approved