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Search: id:A097316
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| A097316 |
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Chebyshev U(n,x) polynomial evaluated at x=33. |
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+0
5
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| 1, 66, 4355, 287364, 18961669, 1251182790, 82559102471, 5447649580296, 359462313197065, 23719065021425994, 1565098829100918539, 103272803655639197580, 6814439942443086121741, 449649763397588044837326
(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 - 17*b^2 =-1. See A078989 with A078988.
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n) = 66*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 66) with S(n, x) := U(n, x/2), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-66*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*66^(n-2*k), k=0..floor(n/2)), n>=0.
a(n) = ((33+8*sqrt(17))^(n+1) - (33-8*sqrt(17))^(n+1))/(16*sqrt(17)).
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CROSSREFS
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Adjacent sequences: A097313 A097314 A097315 this_sequence A097317 A097318 A097319
Sequence in context: A138875 A138877 A004998 this_sequence A099639 A003555 A093266
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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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