A041075 Denominators of continued fraction convergents to sqrt(44).
1, 1, 2, 3, 8, 11, 19, 30, 379, 409, 788, 1197, 3182, 4379, 7561, 11940, 150841, 162781, 313622, 476403, 1266428, 1742831, 3009259, 4752090, 60034339, 64786429, 124820768, 189607197, 504035162, 693642359, 1197677521, 1891319880, 23893516081, 25784835961
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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Magma
I:=[1, 1, 2, 3, 8, 11, 19, 30, 379, 409, 788, 1197, 3182, 4379, 7561, 11940]; [n le 16 select I[n] else 398*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
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Mathematica
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[44],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *) Denominator[Convergents[Sqrt[44], 30]] (* Vincenzo Librandi, Dec 11 2013 *) LinearRecurrence[{0,0,0,0,0,0,0,398,0,0,0,0,0,0,0,-1},{1,1,2,3,8,11,19,30,379,409,788,1197,3182,4379,7561,11940},40] (* Harvey P. Dale, Feb 12 2025 *)
Formula
G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+10*x^4+1) / ((x^8-20*x^4+1)*(x^8+20*x^4+1)). - Colin Barker, Nov 12 2013
a(n) = 398*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 11 2013
Extensions
More terms from Colin Barker, Nov 12 2013