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 A097733 Pell equation solutions (7*b(n))^2 - 2*(5*a(n))^2 = -1 with b(n):=A097732(n), n>=0. Note that D=50=2*5^2 is not squarefree. 4
 1, 197, 39005, 7722793, 1529074009, 302748930989, 59942759261813, 11868363584907985, 2349876047052519217, 465263588952813896981, 92119840736610099083021, 18239263202259846804541177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Tanya Khovanova, Recursive Sequences FORMULA a(n)= S(n, 2*99) - S(n-1, 2*99) = T(2*n+1, 5*sqrt(2))/(5*sqrt(2)), with Chebyshev polynomials of the 2nd 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, 14*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310. G.f.: (1-x)/(1-198*x+x^2). a(n)=198*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=197 . [From Philippe DELEHAM, Nov 18 2008] a(n) = k^n+k^(-n)-a(n-1) = A003499(3n)-a(n-1), where k = (sqrt(2)+1)^6 = 99+70*sqrt(2) and a(0)=1. - Charles L. Hohn, Apr 05 2011 EXAMPLE (x,y) = (7,1), (1393,197), (275807,39005), ... give the positive integer solutions to x^2 - 50*y^2 =-1. CROSSREFS Cf. A097731 for S(n, 198). Row 7 of array A188647. Sequence in context: A201256 A031602 A188361 * A114050 A145452 A025375 Adjacent sequences:  A097730 A097731 A097732 * A097734 A097735 A097736 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 STATUS approved

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