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

0,1

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).

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

Mathematica

Numerator[Convergents[Sqrt[512], 30]] (* Harvey P. Dale, Apr 09 2012 *)

Crossrefs

Cf. A041979, A040489.

Sequence in context: A118297 A022392 A041976 * A041980 A041974 A041972

Adjacent sequences: A041975 A041976 A041977 * A041979 A041980 A041981

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved