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A077243
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Bisection (odd part) of Chebyshev sequence with Diophantine property.
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4
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2, 17, 134, 1055, 8306, 65393, 514838, 4053311, 31911650, 251239889, 1978007462, 15572819807, 122604550994, 965263588145, 7599504154166, 59830769645183, 471046653007298, 3708542454413201, 29197292982298310
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| -5*a(n)^2 + 3* b(n)^2 = 7, with the companion sequence b(n)= A077244(n).
The even part is A077245(n) with Diophantine companion A077246(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)=-1, a(0)=2.
a(n)= 2*S(n, 8)+S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 8)= A001090(n+1).
G.f.: (2+x)/(1-8*x+x^2).
a(n)=[4-sqrt(15)]^n-(3/10)*[4-sqrt(15)]^n*sqrt(15)+[4+sqrt(15)]^n+(3/10)*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*17^2+7 = 1452 = 3*22^2 = 3*A077244(1)^2.
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CROSSREFS
| Sequence in context: A073510 A007354 A180840 * A037525 A037734 A201782
Adjacent sequences: A077240 A077241 A077242 * A077244 A077245 A077246
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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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