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Search: id:A049670
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| 0, 1, 123, 15128, 1860621, 228841255, 28145613744, 3461681649257, 425758697244867, 52364858079469384, 6440451785077489365, 792123204706451722511, 97424713727108484379488
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OFFSET
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0,3
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COMMENT
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Chebyshev polynomials S(n-1,123).
Used for all positive integer solutions of Pell equation x^2 - 5*(5*y)^2 = -4. See A097842 with A097843.
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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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G.f. x/(1-123*x+x^2), 123=L(10)=A000032(10) (Lucas).
a(n+1)= S(n, 123)=U(n, 123/2)= S(2*n+1, 5*sqrt(5))/(5*sqrt(5)), n>=0, 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)=123*a(n-1)-a(n-2), n >= 2; a(0)=0, a(1)=1.
a(n)=(ap^n - am^n)/(ap-am) with ap := (123+55*sqrt(5))/2 and am := (123-55*sqrt(5))/2 = 1/ap.
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PROGRAM
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(Mupad) numlib::fibonacci(10*n)/55 $ n = 0..25; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008
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CROSSREFS
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A column of array A028412.
Sequence in context: A135479 A095761 A121917 this_sequence A033522 A080537 A030492
Adjacent sequences: A049667 A049668 A049669 this_sequence A049671 A049672 A049673
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 20 2000
Chebyshev and Pell comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 10 2004
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