A041051 Denominators of continued fraction convergents to sqrt(31).
1, 1, 2, 7, 37, 118, 155, 273, 2885, 3158, 6043, 21287, 112478, 358721, 471199, 829920, 8770399, 9600319, 18370718, 64712473, 341933083, 1090511722, 1432444805, 2522956527, 26662010075, 29184966602, 55846976677, 196725896633, 1039476459842, 3315155276159
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3040,0,0,0,0,0,0,0,-1).
Programs
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Magma
I:=[1, 1, 2, 7, 37, 118, 155, 273, 2885, 3158, 6043, 21287, 112478, 358721, 471199, 829920]; [n le 16 select I[n] else 3040*Self(n-8) - Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013
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Mathematica
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[31],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*) Denominator[Convergents[Sqrt[31], 30]] (* Vincenzo Librandi, Dec 10 2013 *)
Formula
G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +37*x^10 -118*x^9 +155*x^8 -273*x^7 -155*x^6 -118*x^5 -37*x^4 -7*x^3 -2*x^2 -x -1) / (x^16 -3040*x^8 +1). - Colin Barker, Nov 12 2013
Extensions
More terms from Colin Barker, Nov 12 2013