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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010487, A041052.

Programs

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 *)

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