A041070 Numerators of continued fraction convergents to sqrt(42).
6, 13, 162, 337, 4206, 8749, 109194, 227137, 2834838, 5896813, 73596594, 153090001, 1910676606, 3974443213, 49603995162, 103182433537, 1287793197606, 2678768828749, 33433019142594, 69544807113937
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..100
- Index entries for linear recurrences with constant coefficients, signature (0,26,0,-1).
Programs
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Mathematica
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[42],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*) Numerator[Convergents[Sqrt[42], 30]] (* Vincenzo Librandi, Oct 29 2013 *) LinearRecurrence[{0,26,0,-1},{6,13,162,337},30] (* Harvey P. Dale, Aug 07 2019 *)
Formula
G.f.: -(x+1)*(x^2-7*x-6) / (x^4-26*x^2+1). - Colin Barker, Nov 04 2013