1,2

All positive integer solutions of Pell equation (3*b(n))^2 - 13*a(n)^2 = -4 together with b(n)=A097783(n-1), n>=1.

a(n) = L(n-1,11), where L is defined as in A108299; see also A097783 for L(n,-11). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 01 2005

Number of 01-avoiding words of length n on alphabet {0,1,2,3,4,5,6,7,8,9, A} which do not end in 0. - Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 10 2007

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(1)=1, a(2)=10, and for n>2 a(n)=ceiling(g*f^n) where f=(11+sqrt(117))/2 and g=(1-3/sqrt(13))/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 12 2003

a(n)a(n+3) = 99 + a(n+1)a(n+2). - R. Stephan, May 29 2004

a(n) = S(n-1, 11) - S(n-2, 11) = T(2*n-1, sqrt(13)/2)/(sqrt(13)/2).

a(n+1)= ((-1)^n)*S(2*n, I*3), n>=0, with the imaginary unit I and S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310.

G.f.: x*(1-x)/(1-11*x+x^2).

All positive solutions of the Pell equation x^2 - 13*y^2 = -4 are

(x,y)= (3=3*1,1), (36=3*12,10), (393=3*131,109), (4287=3*1429,1189 ), ...

Row 11 of array A094954.

Adjacent sequences: A078919 A078920 A078921 this_sequence A078923 A078924 A078925

Sequence in context: A059524 A024527 A015591 this_sequence A082181 A095740 A075508

nonn

Nick Renton (ner(AT)nickrenton.com), Jan 11 2003

More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 12 2003