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 A098253 First differences of Chebyshev polynomials S(n,363)=A098251(n) with Diophantine property. 4
 1, 362, 131405, 47699653, 17314842634, 6285240176489, 2281524869222873, 828187242287726410, 300629687425575463957, 109127748348241605689981, 39613072020724277289999146, 14379436015774564414664000017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS (19*b(n))^2 - 365*a(n)^2 = -4 with b(n)=A098252(n) give all positive solutions of this Pell equation. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..389 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (363,-1). FORMULA G.f.: (1 - x)/(1 - 363*x + x^2). a(n) = ((-1)^n)*S(2*n, 19*i) with the imaginary unit i and the S(n, x)=U(n, x/2) Chebyshev polynomials. a(n) = S(n, 363) - S(n-1, 363) = T(2*n+1, sqrt(365)/2)/(sqrt(365)/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) = 363*a(n-1) - a(n-2) for n>1, a(0)=1, a(1)=362. - Philippe Deléham, Nov 18 2008 EXAMPLE All positive solutions of Pell equation x^2 - 365*y^2 = -4 are (19=19*1,1), (6916=19*364,362), (2510489=19*132131,131405), (911300591=19*47963189,47699653), ... CROSSREFS Sequence in context: A200558 A212324 A007565 * A031517 A192449 A116285 Adjacent sequences:  A098250 A098251 A098252 * A098254 A098255 A098256 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Sep 10 2004 STATUS approved

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Last modified October 19 05:08 EDT 2018. Contains 316336 sequences. (Running on oeis4.)