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A041053 Denominators of continued fraction convergents to sqrt(32). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 07:56 EDT 2021. Contains 345416 sequences. (Running on oeis4.)