0,2

(11*b(n))^2 - 5*(5*a(n))^2 = -4 with b(n)=A097842(n) give all positive solutions of this Pell equation.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n)= ((-1)^n)*S(2*n, 11*I) with the imaginary unit I and the S(n, x)=U(n, x/2) Chebyshev polynomials.

G.f.: (1-x)/(1-123*x+x^2).

a(n)= S(n, 123) - S(n-1, 123) = T(2*n+1, 5*sqrt(5)/2)/(5*sqrt(5)/2), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x) and T(n, x) Chebyshev's polynomials of the first kind, A053120.

a(n)=123*a(n-1)-a(n-2) for n>1 ; a(0)=1, a(1)=122. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]

a(n)=(1/2)*{[(123/2)-(55/2)*sqrt(5)]^n+[(123/2)+(55/2)*sqrt(5)]^n}+(11/50)*sqrt(5)*{[(123/2)+(55/2 )*sqrt(5)]^n-[(123/2)-(55/2)*sqrt(5)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Dec 12 2008]

All positive solutions of Pell equation x^2 - 125*y^2 = -4 are

(11=11*1,1), (1364=11*124,122), (167761=11*15251,15005),

(20633239=11*1875749,1845493), ...

Sequence in context: A031599 A131970 A121916 this_sequence A013475 A098129 A013471

Adjacent sequences: A097840 A097841 A097842 this_sequence A097844 A097845 A097846

nonn,easy

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 10 2004