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A077245
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Bisection (even part) of Chebyshev sequence with Diophantine property.
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4
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1, 10, 79, 622, 4897, 38554, 303535, 2389726, 18814273, 148124458, 1166181391, 9181326670, 72284431969, 569094129082, 4480468600687, 35274654676414, 277716768810625, 2186459495808586, 17213959197658063
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 3*b(n)^2 - 5*a(n)^2 = 7, with the companion sequence b(n)= A077246(n).
The odd part is A077243(n) with Diophantine companion A077244(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) := -2, a(0)=1.
a(n)= S(n, 8)+2*S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310. S(-1, x) := 0 and S(n, 8)= A001090(n+1).
G.f.: (1+2*x)/(1-8*x+x^2).
a(n)=(1/2)*[4-sqrt(15)]^n-(1/5)*[4-sqrt(15)]^n*sqrt(15)+(1/2)*[4+sqrt(15)]^n+(1/5)*sqrt(15) *[4+sqrt(15)]^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 08 2008
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EXAMPLE
| 5*a(1)^2 + 7 = 5*10^2 + 7 = 507 = 3*13^2 = 3*A077246(1)^2.
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CROSSREFS
| Sequence in context: A081905 A016138 A006329 * A036732 A206764 A027790
Adjacent sequences: A077242 A077243 A077244 * A077246 A077247 A077248
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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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