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Search: id:A097725
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| A097725 |
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Chebyshev U(n,x) polynomial evaluated at x=51. |
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+0
3
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| 1, 102, 10403, 1061004, 108212005, 11036563506, 1125621265607, 114802332528408, 11708712296632009, 1194173851923936510, 121794024183944892011, 12421796292910455048612
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Used to form integer solutions of Pell equation a^2 - 26*b^2 =-1. See A097726 with A097727.
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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) = 102*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*51)= U(n, 51), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-102*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*102^(n-2*k), k=0..floor(n/2)), n>=0.
a(n) = ((51+10*sqrt(26))^(n+1) - (51-10*sqrt(26))^(n+1))/(20*sqrt(26)).
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CROSSREFS
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Adjacent sequences: A097722 A097723 A097724 this_sequence A097726 A097727 A097728
Sequence in context: A088805 A163435 A030512 this_sequence A129751 A094095 A074675
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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), Aug 31 2004
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