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A102312
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a(n) = Fibonacci(5*n).
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18
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0, 5, 55, 610, 6765, 75025, 832040, 9227465, 102334155, 1134903170, 12586269025, 139583862445, 1548008755920, 17167680177565, 190392490709135, 2111485077978050, 23416728348467685, 259695496911122585, 2880067194370816120, 31940434634990099905
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OFFSET
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0,2
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..950
Michael D.Hirschhorn, A Naive Proof that F5n = 0 (mod 5), Fib. Q. 51(3), 2013, 256-258.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (11,1).
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FORMULA
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G.f.: -5*x/(-1+11*x+x^2).
a(n) = A000045(5*n) = 5*A049666(n).
a(n) = Fibonacci(2*n)*Lucas(3*n)+Fibonacci(n). Lucas =A000032(n), Fibonacci=A000045(n). - Gary Detlefs, Dec 22 2012
a(n) = (-((11 - 5*sqrt(5))/2)^n + ((11+5*sqrt(5))/2)^n)/sqrt(5). - Colin Barker, Nov 10 2016
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MAPLE
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seq(combinat:-fibonacci(5*n), n=0..100); # Robert Israel, Dec 12 2014
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MATHEMATICA
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Table[ Fibonacci[5n], {n, 0, 17}] (* Robert G. Wilson v, Jan 09 2005 *)
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PROG
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(Sage) [fibonacci(5*n) for n in range(0, 18)] # Zerinvary Lajos, May 15 2009
(MAGMA) [Fibonacci(5*n): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011
(PARI) vector(18, n, fibonacci(5*n)) \\ Edward Jiang, Dec 11 2014
(PARI) concat(0, Vec(5*x/(1-11*x-x^2) + O(x^30))) \\ Colin Barker, Nov 10 2016
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CROSSREFS
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Essentially the fifth column of array A102310.
Cf. A049666. [Zerinvary Lajos, May 15 2009]
Cf. A138134 (partial sums).
Sequence in context: A002279 A119292 A139258 * A114909 A038261 A246153
Adjacent sequences: A102309 A102310 A102311 * A102313 A102314 A102315
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan, Jan 06 2005
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STATUS
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approved
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