A041659 Denominators of continued fraction convergents to sqrt(348).

1, 1, 2, 3, 26, 29, 55, 84, 3079, 3163, 6242, 9405, 81482, 90887, 172369, 263256, 9649585, 9912841, 19562426, 29475267, 255364562, 284839829, 540204391, 825044220, 30241796311, 31066840531, 61308636842, 92375477373, 800312455826, 892687933199

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, 3134, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+28*x^4+1) / ((x^8-56*x^4+1)*(x^8+56*x^4+1)). - Colin Barker, Nov 21 2013

a(n) = 3134*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[348], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 26, 29, 55, 84, 3079, 3163, 6242, 9405, 81482, 90887, 172369, 263256]; [n le 16 select I[n] else 3134*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041658, A040329.

Sequence in context: A056004 A032812 A099006 * A042043 A178196 A258766

Adjacent sequences: A041656 A041657 A041658 * A041660 A041661 A041662

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 21 2013

Status

approved