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

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

Author

Bruno Berselli, May 13 2011

Keywords

• nonn
• cofr
• easy

Links

• 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).

Crossrefs

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

Programs

Magma

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

Magma

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

Mathematica

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 *)

PARI

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

Formula

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