A041215 Denominators of continued fraction convergents to sqrt(118).

1, 1, 7, 22, 51, 532, 1115, 3877, 24377, 28254, 589457, 617711, 4295723, 13504880, 31305483, 326559710, 684424903, 2379834419, 14963431417, 17343265836, 361828748137, 379172013973, 2636860831975, 8289754509898, 19216369851771, 200453453027608

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,613834,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +7*x^16 -22*x^15 +51*x^14 -532*x^13 +1115*x^12 -3877*x^11 +24377*x^10 -28254*x^9 -24377*x^8 -3877*x^7 -1115*x^6 -532*x^5 -51*x^4 -22*x^3 -7*x^2 -x -1) / (x^20 -613834*x^10 +1). - Colin Barker, Nov 14 2013

a(n) = 613834*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[118], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)

Prog

(Magma) I:=[1, 1, 7, 22, 51, 532, 1115, 3877, 24377, 28254, 589457, 617711, 4295723, 13504880, 31305483, 326559710, 684424903, 2379834419, 14963431417, 17343265836]; [n le 20 select I[n] else 613834*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041214, A010183.

Sequence in context: A211635 A211634 A184629 * A060822 A011926 A101120

Adjacent sequences: A041212 A041213 A041214 * A041216 A041217 A041218

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved