A040489 -id:A040489 - cp's OEIS frontend

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

N. J. A. Sloane

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).

Cf. A041979, A040489.

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

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

More terms from Colin Barker, Nov 28 2013

A041979 Denominators of continued fraction convergents to sqrt(512).

Original entry on oeis.org

1, 1, 2, 3, 8, 51, 569, 3465, 7499, 10964, 18463, 29427, 1313251, 1342678, 2655929, 3998607, 10653143, 67917465, 757745258, 4614389013, 9986523284, 14600912297, 24587435581, 39188347878, 1748874742213, 1788063090091, 3536937832304, 5325000922395

Offset: 0

N. J. A. Sloane

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).

Cf. A041978, A040489.

Denominator[Convergents[Sqrt[512], 30]] (* Vincenzo Librandi, Jan 11 2014 *)

G.f.: -(x^22 -x^21 +2*x^20 -3*x^19 +8*x^18 -51*x^17 +569*x^16 -3465*x^15 +7499*x^14 -10964*x^13 +18463*x^12 -29427*x^11 -18463*x^10 -10964*x^9 -7499*x^8 -3465*x^7 -569*x^6 -51*x^5 -8*x^4 -3*x^3 -2*x^2 -x -1) / ((x^6 -34*x^3 +1)*(x^6 +34*x^3 +1)*(x^12 +1154*x^6 +1)). - Colin Barker, Nov 28 2013

More terms from Colin Barker, Nov 28 2013

A190567 Continued fraction expansion of 46*sqrt(46).

Original entry on oeis.org

311, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622, 1, 76, 1, 622

Offset: 0

Bruno Berselli, May 13 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
G. Xiao, Contfrac.
Index entries for continued fractions for constants.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A010136; A040005, A040021, A010186, A040201, A040324, A040489, A040968.

[311] cat &cat[ [1,76,1,622]: n in [1..18] ];

I:=[311,1,76,1,622]; [n le 5 select I[n] else Self(n-4): n in [1..80]]; // Vincenzo Librandi, Jun 14 2013

ContinuedFraction[46 Sqrt[46], 80] (* or *) PadRight[{311}, 80, {622, 1, 76, 1}]
CoefficientList[Series[(311 + x + 76 x^2 + x^3 + 311 x^4) / (1 - x^4), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 14 2013 *)

a(n)=if(n,[622,1,76,1][n%4+1],311) \\ Charles R Greathouse IV, May 13 2011

G.f.:  (311+x+76*x^2+x^3+311*x^4)/(1-x^4).
a(n) = 1+3*(1+(-1)^n)*(116+91*i^n)/2 with n>0, i=sqrt(-1) and a(0)=311.
a(n) = (-1513*(n mod 4)+575*((n+1) mod 4)+125*((n+2) mod 4)+2213*((n+3) mod 4))/12  for n>0.
a(n) = a(n-4), n>=5. - Vincenzo Librandi, Jun 14 2013

cp's OEIS Frontend

A041978 Numerators of continued fraction convergents to sqrt(512).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A041979 Denominators of continued fraction convergents to sqrt(512).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A190567 Continued fraction expansion of 46*sqrt(46).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Magma

Mathematica

PARI

Formula