OFFSET
0,1
REFERENCES
Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, page 56. [From Olivier Gérard, May 22 2009]
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).
FORMULA
a(n) = 1 + floor((n+2)/4) - floor((n+1)/4) + 5*(floor((n+4)/4) - floor((n+3)/4)) for n > 0. - Wesley Ivan Hurt, Apr 10 2017
From Amiram Eldar, Nov 12 2023: (Start)
Multiplicative with a(2) = 2, a(2^e) = 6 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 1/2^s + 1/2^(2*s-2)). (End)
EXAMPLE
3.741657386773941385583748732... = 3 + 1/(1 + 1/(2 + 1/(1 + 1/(6 + ...)))). - Harry J. Smith, Jun 02 2009
MATHEMATICA
ContinuedFraction[Sqrt[14], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{3}, 120, {6, 1, 2, 1}] (* Harvey P. Dale, Jan 16 2017 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 15000); x=contfrac(sqrt(14)); for (n=0, 20000, write("b010123.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009
CROSSREFS
KEYWORD
nonn,cofr,easy,mult
AUTHOR
STATUS
approved