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

0,1

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).

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

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 *)

Prog

(Magma)  [311] cat &cat[ [1, 76, 1, 622]: n in [1..18] ];
(PARI) a(n)=if(n, [622, 1, 76, 1][n%4+1], 311) \\ Charles R Greathouse IV, May 13 2011
(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

Crossrefs

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

Sequence in context: A289304 A281568 A084876 * A060339 A046016 A142005

Adjacent sequences: A190564 A190565 A190566 * A190568 A190569 A190570

Keyword

nonn,cofr,easy

Author

Bruno Berselli, May 13 2011

Status

approved