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A097512
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6*Lucas(2n) - Fib(2n+2).
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1
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11, 15, 34, 87, 227, 594, 1555, 4071, 10658, 27903, 73051, 191250, 500699, 1310847, 3431842, 8984679, 23522195, 61581906, 161223523, 422088663, 1105042466, 2893038735, 7574073739, 19829182482, 51913473707, 135911238639
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Sequence relates bisections of Lucas and Fibonacci numbers.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n) = 8*Lucas(2n) - Lucas(2n+2) - 2*Fib(2n-1) = 8*A005248(n) - A005248(n+1) - 2*A001519(n).
a(n+1)/a(n) approaches the golden ratio phi + 1 = (3+sqrt(5))/2.
a(n)=3*a(n-1)-a(n-2) with a(0)=11 and a(1)=15. G.f.: (11-18x)/(1-3x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008]
a(n)=(11/2)*[(3/2)+(1/2)*sqrt(5)]^n-(3/10)*[(3/2)+(1/2)*sqrt(5)]^n*sqrt(5)+(3/10)*[(3/2)-(1/2) *sqrt(5)]^n*sqrt(5)+(11/2)*[(3/2)-(1/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 19 2008]
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MATHEMATICA
| Table[6LucasL[2n]-Fibonacci[2n+2], {n, 0, 30}] (* or *) LinearRecurrence[ {3, -1}, {11, 15}, 30] (* From Harvey P. Dale, Oct 02 2011 *)
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PROG
| (MAGMA) [8*Lucas(2*n) - Lucas(2*n+2) - 2*Fibonacci(2*n-1): n in [0..30]]; // Vincenzo Librandi, Oct 03 2011
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CROSSREFS
| Cf. A005248, A005248, A022133.
Sequence in context: A009433 A030099 A085597 * A032490 A068483 A115779
Adjacent sequences: A097509 A097510 A097511 * A097513 A097514 A097515
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KEYWORD
| nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 26 2004
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EXTENSIONS
| New definition from Ralf Stephan, Dec 01, 2004
More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2009
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