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A081013
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Fibonacci(4n+3)-2, or Fibonacci(2n)*Lucas(2n+3).
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0
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0, 11, 87, 608, 4179, 28655, 196416, 1346267, 9227463, 63245984, 433494435, 2971215071, 20365011072, 139583862443, 956722026039, 6557470319840, 44945570212851, 308061521170127, 2111485077978048, 14472334024676219
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (8,-8,1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 03 2010]
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FORMULA
| a(n) = 8a(n-1)-8a(n-2)+a(n-3)
a(n)=-2+[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n+(2/5)*sqrt(5)*[(7/2)+(3/2)*sqrt(5)]^n-[(7/2)-(3/2)*sqrt(5)]^n}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Dec 01 2008]
G.f.: x*(-11+x) / ( (x-1)*(x^2-7*x+1) ). a(n) = A033891(n)-2. a(n+1)-a(n) = A056914(n+1), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 03 2010]
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MAPLE
| with(combinat) for n from 0 to 25 do printf(`%d, `, fibonacci(4*n+3)-2) od
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PROG
| (MAGMA) [Fibonacci(4*n+3)-2: n in [0..50]]; // Vincenzo Librandi, Apr 20 2011
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CROSSREFS
| Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
Sequence in context: A014917 A080962 A016222 * A163616 A119383 A001278
Adjacent sequences: A081010 A081011 A081012 * A081014 A081015 A081016
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KEYWORD
| nonn,easy
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AUTHOR
| R. K. Guy (rkg(AT)cpsc.ucalgary.ca), Mar 01, 2003
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EXTENSIONS
| More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Mar 03, 2003
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