A041074 Numerators of continued fraction convergents to sqrt(44).
6, 7, 13, 20, 53, 73, 126, 199, 2514, 2713, 5227, 7940, 21107, 29047, 50154, 79201, 1000566, 1079767, 2080333, 3160100, 8400533, 11560633, 19961166, 31521799, 398222754, 429744553, 827967307, 1257711860
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,398,0,0,0,0,0,0,0,-1).
Programs
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Mathematica
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[44],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*) Numerator[Convergents[Sqrt[44], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
Formula
G.f.: -(x^15 -6*x^14 +7*x^13 -13*x^12 +20*x^11 -53*x^10 +73*x^9 -126*x^8 -199*x^7 -126*x^6 -73*x^5 -53*x^4 -20*x^3 -13*x^2 -7*x -6) / ((x^8 -20*x^4 +1)*(x^8 +20*x^4 +1)). - Colin Barker, Nov 04 2013