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Search: id:A098257
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| A098257 |
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Chebyshev polynomials S(n,531). |
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+0
3
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| 1, 531, 281960, 149720229, 79501159639, 42214966048080, 22416067470370841, 11902889611800868491, 6320411967798790797880, 3356126852011546112805789, 1782097038006163187109076079, 946290171054420640808806592160
(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 - 533*y^2 = -4. See A098258 with A098259.
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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, 531)=U(n, 531/2)= S(2*n+1, sqrt(533))/sqrt(533) 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)=531*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=531; a(-1):=0.
a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (531+23*sqrt(533))/2 and am := (531-23*sqrt(533))/2 = 1/ap.
G.f.: 1/(1-531*x+x^2).
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CROSSREFS
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Sequence in context: A031967 A031521 A031701 this_sequence A048055 A067803 A098258
Adjacent sequences: A098254 A098255 A098256 this_sequence A098258 A098259 A098260
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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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