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 A097315 Pell equation solutions (3*b(n))^2 - 10*a(n)^2 = -1 with b(n):=A097314(n), n>=0. 9
 1, 37, 1405, 53353, 2026009, 76934989, 2921503573, 110940200785, 4212806126257, 159975692596981, 6074863512559021, 230684837784645817, 8759948972303982025, 332647376109766671133, 12631840343198829521029 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Hypotenuses of primitive Pythagorean triples in A195616 and A195617. - Clark Kimberling, Sep 22 2011 LINKS Tanya Khovanova, Recursive Sequences FORMULA a(n)= S(n, 38) - S(n-1, 38) = T(2*n+1, sqrt(10))/sqrt(10), with Chebyshev polynomials of the second and first kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x); and A053120 for the T-triangle. a(n)= ((-1)^n)*S(2*n, 6*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310. G.f.: (1-x)/(1-38*x+x^2). a(n)=38*a(n-1)-a(n-2) for n>1 ; a(0)=1, a(1)=37. [From Philippe DELEHAM, Nov 18 2008] EXAMPLE (x,y) = (3,1), (117,37), (4443,1405),... give the positive integer solutions to x^2 - 10*y^2 =-1. CROSSREFS Row 3 of array A188647. Cf. A221874. Sequence in context: A207185 A189061 A009981 * A158741 A094490 A009695 Adjacent sequences:  A097312 A097313 A097314 * A097316 A097317 A097318 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 EXTENSIONS Typo in recurrence formula corrected Laurent Bonaventure (bonave(AT)free.fr), Oct 03 2010 STATUS approved

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