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A077234
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Bisection (odd part) of Chebyshev sequence with Diophantine property.
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4
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2, 9, 34, 127, 474, 1769, 6602, 24639, 91954, 343177, 1280754, 4779839, 17838602, 66574569, 248459674, 927264127, 3460596834, 12915123209, 48199896002, 179884460799, 671337947194, 2505467327977, 9350531364714, 34896658130879
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| -3*a(n)^2 + b(n)^2 = 13, with the companion sequence b(n)= A077235(n).
The even part is A054491(n) with Diophantine companion A077236(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)= 2*S(n, 4)+S(n-1, 4), with S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(-1, x) := 0 and S(n, 4)= A001353(n+1).
G.f.: (2+x)/(1-4*x+x^2).
a(n)=4*a(n-1)-a(n-2) with a(0)=2 and a(1)=9. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008]
a(n)=-(5/6)*sqrt(3)*[2-sqrt(3)]^n+(5/6)*sqrt(3)*[2+sqrt(3)]^n+[2-sqrt(3)]^n+[2+sqrt(3)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 20 2008]
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EXAMPLE
| 3*a(1)^2 + 13 = 3*81+13 = 256 = 16^2 = A077235(1)^2.
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CROSSREFS
| Cf. A077237 (even and odd parts).
Sequence in context: A000524 A120989 A010763 * A091526 A204444 A204430
Adjacent sequences: A077231 A077232 A077233 * A077235 A077236 A077237
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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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