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A001060
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a(n) = a(n-1) + a(n-2).
(Formerly M1338 N0512)
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10
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2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, 898, 1453, 2351, 3804, 6155, 9959, 16114, 26073, 42187, 68260, 110447, 178707, 289154, 467861, 757015, 1224876, 1981891, 3206767, 5188658, 8395425, 13584083, 21979508, 35563591, 57543099
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| From a(2) on, sums of five consecutive Fibonacci numbers; the subset of primes is essentially in A153892. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 24 2010]
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REFERENCES
| A. Brousseau, Seeking the lost gold mine or exploring Fibonacci factorizations, Fib. Quart., 3 (1965), 129-130.
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 52.
R. V. Jean, Mathematical Approach to Pattern and Form in Plant Growth, Wiley, 1984. See p. 5. [From N. J. A. Sloane, Jun 08 2011]
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n)=2*fibonacci(n-3)+fibonacci(n), n>=3. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 05 2007
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MAPLE
| with(combinat):a:=n->2*fibonacci(n-3)+fibonacci(n): seq(a(n), n=3..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 05 2007
A001060:=-(2+3*z)/(-1+z+z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[a=Fibonacci[n+5]-Fibonacci[n], {n, -1, 60}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 23 2009]
LinearRecurrence[{1, 1}, {2, 5}, 50] (* Vincenzo Librandi, Jan 16 2012 *)
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PROG
| (MAGMA) I:=[2, 5]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 16 2012
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CROSSREFS
| Apart from initial term, same as A013655.
Sequence in context: A005895 A135525 A117538 * A042343 A042691 A112732
Adjacent sequences: A001057 A001058 A001059 * A001061 A001062 A001063
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 04 2000
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