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A097767
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Pell equation solutions (11*b(n))^2 - 122*a(n)^2 = -1 with b(n):=A097766(n), n>=0.
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4
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1, 485, 235709, 114554089, 55673051545, 27056988496781, 13149640736384021, 6390698340894137425, 3105866244033814404529, 1509444603902092906463669, 733586971630173118726938605, 356521758767660233608385698361
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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*243) - S(n-1, 2*243) = T(2*n+1, sqrt(122))/sqrt(122), 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, 22*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1-486*x+x^2).
a(n)=486*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=485 . [From Philippe DELEHAM, Nov 18 2008]
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EXAMPLE
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(x,y) = (11*1=11;1), (5357=11*487;485), (2603491=11*236681;235709), ... give the positive integer solutions to x^2 - 122*y^2 =-1.
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CROSSREFS
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Cf. A097765 for S(n, 486).
Row 11 of array A188647.
Sequence in context: A031722 A031610 A156774 * A031520 A130181 A158325
Adjacent sequences: A097764 A097765 A097766 * A097768 A097769 A097770
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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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