0,2

All positive integer solutions of Pell equation (3*a(n))^2 - 13*b(n)^2 = -4 together with b(n)=A078922(n+1), n>=0.

a(n) = L(n,-11)*(-1)^n, where L is defined as in A108299; see also A078922 for L(n,+11). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n)= S(n, 11) +S(n-1, 11) = S(2*n, sqrt(13)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the 2nd kind, A049310. S(-1, x)= 0 = U(-1, x).

a(n)= (-2/3)*I*((-1)^n)*T(2*n+1, 3*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120.

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

a(n)=11*a(n-1)-a(n-2) with a(0)=1 and a(1)=12. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]

All positive solutions to the Pell equation x^2 - 13*y^2 = -4 are (3=3*1,1), (36=3*12,10), (393=3*131,109), (4287=3*1429,1189 ), ...

(Other) sage: [(lucas_number2(n, 11, 1)-lucas_number2(n-1, 11, 1))/9 for n in xrange(1, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]

Cf. S(n, 11)=A004190(n).

Sequence in context: A163414 A111777 A160962 this_sequence A078218 A048643 A111085

Adjacent sequences: A097780 A097781 A097782 this_sequence A097784 A097785 A097786

nonn,easy,new

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004