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Search: id:A097834
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| A097834 |
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Chebyshev polynomials S(n,27) + S(n-1,27) with diophantine property. |
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+0
2
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| 1, 28, 755, 20357, 548884, 14799511, 399037913, 10759224140, 290100013867, 7821941150269, 210902311043396, 5686540457021423, 153325690028535025, 4134107090313424252, 111467565748433919779, 3005490168117402409781
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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(5*a(n))^2 - 29*b(n)^2 = -4 with b(n)=A097835(n) give all positive solutions of this Pell equation.
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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, 27) + S(n-1, 27) = S(2*n, sqrt(29)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 27)=A097781(n).
a(n)= (-2/5)*I*((-1)^n)*T(2*n+1, 5*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120.
G.f.: (1+x)/(1-27*x+x^2).
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EXAMPLE
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All positive solutions of Pell equation x^2 - 29*y^2 = -4 are
(5=5*1,1), (140=5*28,26), (3775=5*755,701), (101785=5*20357,18901), ...
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CROSSREFS
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Sequence in context: A070310 A004293 A012808 this_sequence A063817 A113532 A097311
Adjacent sequences: A097831 A097832 A097833 this_sequence A097835 A097836 A097837
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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), Sep 10 2004
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