A041052 Numerators of continued fraction convergents to sqrt(32).

5, 6, 11, 17, 181, 198, 379, 577, 6149, 6726, 12875, 19601, 208885, 228486, 437371, 665857, 7095941, 7761798, 14857739, 22619537, 241053109, 263672646, 504725755, 768398401, 8188709765, 8957108166, 17145817931, 26102926097, 278175078901, 304278004998

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,34,0,0,0,-1).

Crossrefs

Cf. A010487, A041053.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[32], n]]], {n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
Numerator[Convergents[Sqrt[32], 30]] (* Vincenzo Librandi, Oct 23 2013 *)

Formula

G.f.: (5+6*x+11*x^2+17*x^3+11*x^4-6*x^5+5*x^6-x^7)/(1-34*x^4+x^8). - Colin Barker, Jan 03 2012