A041053 Denominators of continued fraction convergents to sqrt(32).

1, 1, 2, 3, 32, 35, 67, 102, 1087, 1189, 2276, 3465, 36926, 40391, 77317, 117708, 1254397, 1372105, 2626502, 3998607, 42612572, 46611179, 89223751, 135834930, 1447573051, 1583407981, 3030981032, 4614389013

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,34,0,0,0,-1).

Formula

G.f.: (1+x+2*x^2+3*x^3-2*x^4+x^5-x^6)/(1-34*x^4+x^8). [Colin Barker, Mar 13 2012]

a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=32, a(5)=35, a(6)=67, a(7)=102, a(n)=34*a(n-4)-a(n-8). - Harvey P. Dale, Jun 15 2015

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[32], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*)
Denominator[Convergents[Sqrt[32], 30]] (* or *) LinearRecurrence[{0, 0, 0, 34, 0, 0, 0, -1}, {1, 1, 2, 3, 32, 35, 67, 102}, 30] (* Harvey P. Dale, Jun 15 2015 *)

Crossrefs

Cf. A010487, A041052.

Sequence in context: A173353 A032815 A176894 * A212763 A103108 A107124

Adjacent sequences: A041050 A041051 A041052 * A041054 A041055 A041056

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved