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Search: id:A098248
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| A098248 |
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Chebyshev polynomials S(n,291). |
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+0
2
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| 1, 291, 84680, 24641589, 7170617719, 2086625114640, 607200737742521, 176693328057958971, 51417151264128318040, 14962214324533282590669, 4353952951287921105566639, 1266985346610460508437301280
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Used for all positive integer solutions of Pell equation x^2 - 293*y^2 = -4. See A098249 with A098250.
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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, 291)=U(n, 291/2)= S(2*n+1, sqrt(293))/sqrt(293) with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x).
a(n)=291*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=291; a(-1):=0.
a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (291+17*sqrt(293))/2 and am := (291-17*sqrt(293))/2 = 1/ap.
G.f.: 1/(1-291*x+x^2).
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CROSSREFS
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Sequence in context: A031695 A158254 A088892 this_sequence A048956 A043439 A098249
Adjacent sequences: A098245 A098246 A098247 this_sequence A098249 A098250 A098251
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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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