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Search: id:A098251
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| A098251 |
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Chebyshev polynomials S(n,363). |
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+0
3
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| 1, 363, 131768, 47831421, 17362674055, 6302602850544, 2287827472073417, 830475069759799827, 301460162495335263784, 109429208510736940953765, 39722501229235014230952911, 14419158517003799428894952928
(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 - 365*y^2 = -4. See A098252 with A098253.
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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, 363)=U(n, 363/2)= S(2*n+1, sqrt(365))/sqrt(365) 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)=363*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=363; a(-1):=0.
a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (363+19*sqrt(365))/2 and am := (363-19*sqrt(365))/2 = 1/ap.
G.f.: 1/(1-363*x+x^2).
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CROSSREFS
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Adjacent sequences: A098248 A098249 A098250 this_sequence A098252 A098253 A098254
Sequence in context: A031517 A116285 A031697 this_sequence A115464 A004534 A023697
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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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