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A110391
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a(n) = L(3n)/L(n), where L(n) = Lucas number.
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8
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1, 4, 6, 19, 46, 124, 321, 844, 2206, 5779, 15126, 39604, 103681, 271444, 710646, 1860499, 4870846, 12752044, 33385281, 87403804, 228826126, 599074579, 1568397606, 4106118244, 10749957121, 28143753124, 73681302246, 192900153619
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Subsidiary sequences: a(n) = L((2k+1)*n)/L(n) for k = 2,3, etc. This is the sequence for k =1.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,2,-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2010]
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FORMULA
| a(n) = A005248(n)-(-1)^n = +2*a(n-1) +2*a(n-2) -a(n-3). G.f.: ( 1+2*x-4*x^2 ) / ( (1+x)*(x^2-3*x+1) ) [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2010]
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EXAMPLE
| a(1)=L(3)/L(1)=4/1=4.
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MAPLE
| with(combinat): L:=n->fibonacci(n+2)-fibonacci(n-2): seq(L(3*n)/L(n), n=0..30); (Deutsch)
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CROSSREFS
| Cf. A000204.
Sequence in context: A006534 A064035 A010364 * A197460 A001683 A053892
Adjacent sequences: A110388 A110389 A110390 * A110392 A110393 A110394
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KEYWORD
| easy,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 27 2005
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EXTENSIONS
| Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu) and Erich Friedman (efriedma(AT)stetson.edu), Jul 31 2005
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