0,2

Chebyshev's polynomials T(n,x) evaluated at x=6.

a(n+1) give all (nontrivial, integer) solutions of Pell equation a(n+1)^2 - 35*b(n)^2 = +1 with b(n)=A004191(n), n>=0.

a(35+70k)-1 and a(35+70k)+1 are consecutive odd powerful numbers. The first pair is 23101441813552306872262673994181386126+-1. See A076445. - T. D. Noe (noe(AT)sspectra.com), May 04 2006

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) = T(n, 6) = (S(n, 12)-S(n-2, 12))/2 with S(n, x) := U(n, x/2) and T(n), resp. U(n, x), are Chebyshev's polynomials of the first, resp. second, kind. See A053120 and A049310. S(-2, x) := -1, S(-1, x) := 0, S(n, 12)=A004191(n).

a(n) = ((6+sqrt(35))^n + (6-sqrt(35))^n)/2.

G.f.: (1-6*x)/(1-12*x+x^2).

a(n)a(n+3) - a(n+1)a(n+2) = 420. - R. Stephan, Jun 06 2005

Cf. A087800.

Sequence in context: A050788 A027317 A099339 this_sequence A092660 A092085 A028844

Adjacent sequences: A023035 A023036 A023037 this_sequence A023039 A023040 A023041

nonn

David W. Wilson (davidwwilson(AT)comcast.net)

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002