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 A098291 Chebyshev polynomials S(n,731) + S(n-1,731) with Diophantine property. 2
 1, 732, 535091, 391150789, 285930691668, 209014944458519, 152789638468485721, 111689016705518603532, 81644518422095630696171, 59682031277535200520297469, 43627483219359809484706753668 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS (27*a(n))^2 - 733*b(n)^2 = -4 with b(n)=A098292(n) give all positive solutions of this Pell equation. LINKS Tanya Khovanova, Recursive Sequences Giovanni Lucca, Integer Sequences and Circle Chains Inside a Hyperbola, Forum Geometricorum (2019) Vol. 19, 11-16. Index entries for linear recurrences with constant coefficients, signature (731,-1). FORMULA a(n) = S(n, 731) + S(n-1, 731) = S(2*n, sqrt(733)), with S(n, x) = U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 731)=A098263(n). a(n) = (-2/27)*i*((-1)^n)*T(2*n+1, 27*i/2) with the imaginary unit i and Chebyshev's polynomials of the first kind. See the T-triangle A053120. G.f.: (1+x)/(1-731*x+x^2). EXAMPLE All positive solutions of Pell equation x^2 - 733*y^2 = -4 are (27=27*1,1), (19764=27*732,730), (14447457=27*535091,533629), (10561071303=27*391150789,390082069), ... CROSSREFS Cf. A098292. Sequence in context: A158396 A098263 A289571 * A255798 A044988 A288882 Adjacent sequences:  A098288 A098289 A098290 * A098292 A098293 A098294 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Sep 10 2004 STATUS approved

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Last modified October 20 23:28 EDT 2020. Contains 337910 sequences. (Running on oeis4.)