A041051 Denominators of continued fraction convergents to sqrt(31).

1, 1, 2, 7, 37, 118, 155, 273, 2885, 3158, 6043, 21287, 112478, 358721, 471199, 829920, 8770399, 9600319, 18370718, 64712473, 341933083, 1090511722, 1432444805, 2522956527, 26662010075, 29184966602, 55846976677, 196725896633, 1039476459842, 3315155276159

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3040,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +37*x^10 -118*x^9 +155*x^8 -273*x^7 -155*x^6 -118*x^5 -37*x^4 -7*x^3 -2*x^2 -x -1) / (x^16 -3040*x^8 +1). - Colin Barker, Nov 12 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[31], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*)
Denominator[Convergents[Sqrt[31], 30]] (* Vincenzo Librandi, Dec 10 2013 *)

Prog

(Magma) I:=[1, 1, 2, 7, 37, 118, 155, 273, 2885, 3158, 6043, 21287, 112478, 358721, 471199, 829920]; [n le 16 select I[n] else 3040*Self(n-8) - Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013

Crossrefs

Cf. A041050, A010129, A020788, A010486.

Sequence in context: A173827 A029990 A042465 * A175487 A216362 A002787

Adjacent sequences: A041048 A041049 A041050 * A041052 A041053 A041054

Keyword

nonn,cofr,easy,frac

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved