A041978 Numerators of continued fraction convergents to sqrt(512).
22, 23, 45, 68, 181, 1154, 12875, 78404, 169683, 248087, 417770, 665857, 29715478, 30381335, 60096813, 90478148, 241053109, 1536796802, 17145817931, 104411704388, 225969226707, 330380931095, 556350157802, 886731088897, 39572518069270, 40459249158167
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1331714,0,0,0,0,0,0,0,0,0,0,0,-1).
Programs
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Mathematica
Numerator[Convergents[Sqrt[512], 30]] (* Harvey P. Dale, Apr 09 2012 *)
Formula
G.f.: -(x^23 -22*x^22 +23*x^21 -45*x^20 +68*x^19 -181*x^18 +1154*x^17 -12875*x^16 +78404*x^15 -169683*x^14 +248087*x^13 -417770*x^12 -665857*x^11 -417770*x^10 -248087*x^9 -169683*x^8 -78404*x^7 -12875*x^6 -1154*x^5 -181*x^4 -68*x^3 -45*x^2 -23*x -22) / ((x^6 -34*x^3 +1)*(x^6 +34*x^3 +1)*(x^12 +1154*x^6 +1)). - Colin Barker, Nov 28 2013
Limit n->infinity a(n)^(1/n) = (1+sqrt(2))^(4/3) = 3.2386765777... - Vaclav Kotesovec, Nov 28 2013
Extensions
More terms from Colin Barker, Nov 28 2013