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 A097835 First differences of Chebyshev polynomials S(n,27)=A097781(n) with Diophantine property. 5
 1, 26, 701, 18901, 509626, 13741001, 370497401, 9989688826, 269351100901, 7262490035501, 195817879857626, 5279820266120401, 142359329305393201, 3838422070979496026, 103495036587140999501, 2790527565781827490501 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS (5*b(n))^2 - 29*a(n)^2 = -4 with b(n)=A097834(n) give all positive solutions of this Pell equation. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..697 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (27, -1). FORMULA a(n)= ((-1)^n)*S(2*n, 5*I) with the imaginary unit I and the S(n, x)=U(n, x/2) Chebyshev polynomials. G.f.: (1-x)/(1-27*x+x^2). a(n)= S(n, 27) - S(n-1, 27) = T(2*n+1, sqrt(29)/2)/(sqrt(29)/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)=27*a(n-1)-a(n-2), a(0)=1, a(1)=26. [From Philippe Deléham, Nov 18 2008] EXAMPLE All positive solutions of Pell equation x^2 - 29*y^2 = -4 are (5=5*1,1), (140=5*28,26), (3775=5*755,701), (101785=5*20357,18901), ... MATHEMATICA LinearRecurrence[{27, -1}, {1, 26}, 30] (* Harvey P. Dale, May 31 2013 *) CROSSREFS Cf. similar sequences listed in A238379. Sequence in context: A041313 A042302 A031423 * A158643 A181227 A094738 Adjacent sequences:  A097832 A097833 A097834 * A097836 A097837 A097838 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Sep 10 2004 STATUS approved

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Last modified December 12 17:10 EST 2018. Contains 318079 sequences. (Running on oeis4.)