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Search: id:A098254
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| A098254 |
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Chebyshev polynomials S(n,443). |
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+0
3
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| 1, 443, 196248, 86937421, 38513081255, 17061208058544, 7558076656853737, 3348210897778146947, 1483249869639062243784, 657076344039206795849365, 291083337159498971499024911, 128949261285314005167272186208
(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 - 445*y^2 = -4. See A098255 with A098256.
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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, 443)=U(n, 443/2)= S(2*n+1, sqrt(445))/sqrt(445) 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)=443*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=443; a(-1):=0.
a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (443+21*sqrt(445))/2 and am := (443-21*sqrt(445))/2 = 1/ap.
G.f.: 1/(1-443*x+x^2).
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CROSSREFS
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Adjacent sequences: A098251 A098252 A098253 this_sequence A098255 A098256 A098257
Sequence in context: A105980 A031519 A031699 this_sequence A111496 A128675 A043507
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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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