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Search: id:A097773
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| A097773 |
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Pell equation solutions (13*b(n))^2 - 170*a(n)^2 = -1 with b(n):=A097772(n), n>=0. |
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3
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| 1, 677, 459005, 311204713, 210996336409, 143055204880589, 96991217912702933, 65759902689607707985, 44585117032336113310897, 30228643588021195217080181, 20494975767561338021067051821
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= ((-1)^n)*S(2*n, 26*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1-678*x+x^2).
a(n)= S(n, 2*339) - S(n-1, 2*339) = T(2*n+1, sqrt(170))/sqrt(170), 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.
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EXAMPLE
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(x,y) = (13*1=13;1), (8827=13*679;677), (5984693=13*460361;459005), ... give the positive integer solutions to x^2 - 170*y^2 =-1.
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CROSSREFS
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Cf. A097771 for S(n, 678).
Sequence in context: A031614 A031730 A108824 this_sequence A031524 A097771 A121105
Adjacent sequences: A097770 A097771 A097772 this_sequence A097774 A097775 A097776
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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