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Search: id:A097742
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| A097742 |
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Pell equation solutions (10*b(n))^2 - 101*a(n)^2 = -1 with b(n):=A097741(n), n>=0. |
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+0
4
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| 1, 401, 161201, 64802401, 26050404001, 10472197606001, 4209797387208401, 1692328077460171201, 680311677341601614401, 273483601963246388818001, 109939727677547706703222001, 44195497042772214848306426401
(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)= S(n, 2*201) - S(n-1, 2*201) = T(2*n+1, sqrt(101))/sqrt(101), 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, 20*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1-402*x+x^2).
a(n)=402*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=401 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
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(x,y) = (10*1=10;1), (4030=10*403;401), (1620050=10*162005;161201), ... give the positive integer solutions to x^2 - 101*y^2 =-1.
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CROSSREFS
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Cf. A097740 for S(n, 402).
Sequence in context: A031608 A102324 A156785 this_sequence A115244 A031518 A104391
Adjacent sequences: A097739 A097740 A097741 this_sequence A097743 A097744 A097745
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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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