A041095 Denominators of continued fraction convergents to sqrt(55).
1, 2, 5, 12, 173, 358, 889, 2136, 30793, 63722, 158237, 380196, 5480981, 11342158, 28165297, 67672752, 975583825, 2018840402, 5013264629, 12045369660, 173648439869, 359342249398, 892332938665, 2144008126728, 30908446712857, 63960901552442, 158830249817741
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,178,0,0,0,-1).
Programs
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Magma
I:=[1, 2, 5, 12, 173, 358, 889, 2136]; [n le 8 select I[n] else 178*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
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Mathematica
Denominator[Convergents[Sqrt[55], 30]] (* Vincenzo Librandi, Dec 11 2013 *) LinearRecurrence[{0,0,0,178,0,0,0,-1},{1,2,5,12,173,358,889,2136},30] (* Harvey P. Dale, Nov 24 2022 *)
Formula
G.f.: -(x^2-2*x-1)*(x^4+6*x^2+1) / (x^8-178*x^4+1). - Colin Barker, Nov 12 2013
a(n) = 178*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013
Extensions
More terms from Colin Barker, Nov 12 2013