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A077246
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Bisection (even part) of Chebyshev sequence with Diophantine property.
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4
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2, 13, 102, 803, 6322, 49773, 391862, 3085123, 24289122, 191227853, 1505533702, 11853041763, 93318800402, 734697361453, 5784260091222, 45539383368323, 358530806855362, 2822707071474573, 22223125764941222
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 3*a(n)^2 - 5*b(n)^2 = 7, with the companion sequence b(n)= A077245(n).
The odd part is A077244(n) with Diophantine companion A077243(n).
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)= 8*a(n-1) - a(n-2), a(-1) := 3, a(0)=2.
a(n)= (T(n+1, 4)+2*T(n, 4))/3, with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 4)= A001091(n).
G.f.: (2-3*x)/(1-8*x+x^2).
a(n)=[4-sqrt(15)]^n-(1/6)*[4-sqrt(15)]^n*sqrt(15)+[4+sqrt(15)]^n+(1/6)*sqrt(15)*[4 +sqrt(15)]^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 08 2008
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EXAMPLE
| 13 = a(1) = sqrt((5*A077245(1)^2 + 7)/3) = sqrt((5*10^2 + 7)/3) = sqrt(169) = 13.
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CROSSREFS
| Sequence in context: A123619 A030519 A141116 * A107000 A046891 A046893
Adjacent sequences: A077243 A077244 A077245 * A077247 A077248 A077249
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002
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