0,3

Continued fraction for sqrt(3).

Also coefficient of the highest power of q in the expansion of the polynomial nu(n) defined by: nu(0)=1, nu(1)=b and for n>=2, nu(n)=b*nu(n-1)+lambda*(n-1)_q*nu(n-2) with (b,lambda)=(1,1), where (n)_q=(1+q+...+q^(n-1)) and q is a root of unity. - Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

nu(0)=1 nu(1)=1; nu(2)=2; nu(3)=3+q; nu(4)=5+3q+2q^2; nu(5)=8+7q+6q^2+4q^3+q^4; nu(6)=13+15q+16q^2+14q^3+11q^4+5q^5+2q^6.

M. Beattie, S. D\u{a}sc\u{a}lescu and S. Raianu, Lifting of Nichols Algebras of Type B_2

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

G. Xiao, Contfrac

Index entries for continued fractions for constants

Eric Weisstein's World of Mathematics, Theodorus's Constant

Multiplicative with a(p^e) = 2 if p even; 1 if p odd. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.

G.f.: (1+x+x^2)/(1-x^2). E.g.f.: (3exp(x)-2exp(0)+exp(-x))/2. - Paul Barry (pbarry(AT)wit.ie), Apr 27 2003

a(n)=(3-2*0^n +(-1)^n)/2. a(-n)=a(n). a(2n+1)=1, a(2n)=2, n nonzero.

a(n)=sum{k=0..n, F(n-k+1)*(-2+(1+(-1)^k)/2+C(2, k)+0^k)}; - Paul Barry (pbarry(AT)wit.ie), Jun 22 2007

Row sums of triangle A133566 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 16 2007

a(n)=3/2+(1/2)*(-1)^n-[C(2*n,n) mod 2], with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 27 2007

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):

(PARI) a(n)=2-(n==0)-(n%2)

Cf. A133566.

Adjacent sequences: A039998 A039999 A040000 this_sequence A040002 A040003 A040004

Sequence in context: A022927 A063435 A000034 this_sequence A134451 A066788 A023126

nonn,cofr,easy,mult

njas