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A097733
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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.
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4
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1, 197, 39005, 7722793, 1529074009, 302748930989, 59942759261813, 11868363584907985, 2349876047052519217, 465263588952813896981, 92119840736610099083021, 18239263202259846804541177
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..11.
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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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
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EXAMPLE
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(x,y) = (7,1), (1393,197), (275807,39005), ... give the positive integer solutions to x^2 - 50*y^2 =-1.
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Aug 31 2004
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STATUS
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approved
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