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A097316
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Chebyshev U(n,x) polynomial evaluated at x=33.
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5
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1, 66, 4355, 287364, 18961669, 1251182790, 82559102471, 5447649580296, 359462313197065, 23719065021425994, 1565098829100918539, 103272803655639197580, 6814439942443086121741, 449649763397588044837326
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OFFSET
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0,2
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COMMENTS
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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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Indranil Ghosh, Table of n, a(n) for n = 0..548
R. Flórez, R. A. Higuita, A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (66, -1).
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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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MATHEMATICA
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LinearRecurrence[{66, -1}, {1, 66}, 14] (* Ray Chandler, Aug 11 2015 *)
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CROSSREFS
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Sequence in context: A265454 A004998 A239409 * A239337 A099639 A003555
Adjacent sequences: A097313 A097314 A097315 * A097317 A097318 A097319
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Aug 31 2004
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STATUS
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approved
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