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Search: id:A060280
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| A060280 |
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Number of orbits of length n under the map whose periodic points are counted by A001350. |
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+0
3
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| 1, 0, 1, 1, 2, 2, 4, 5, 8, 11, 18, 25, 40, 58, 90, 135, 210, 316, 492, 750, 1164, 1791, 2786, 4305, 6710, 10420, 16264, 25350, 39650
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Euler transform is Fibonacci(n). 1/((1-x)(1-x^3)(1-x^4)(1-x^5)^2(1-x^6)^2...)=1+x+x^2+2x^3+3x^4+5x^5+8x^6+...
Baake, Roberts and Weiss [2008] explicitly cite A060280 and A001350 on p.9 and show A060280 in Table 1, Fixed point and orbit counts for the golden cat map, p.10; OEIS being footnote 38, p.22. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 27 2008]
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REFERENCES
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Baake, Michael; Hermisson, Joachim; Pleasants, Peter A. B.; The torus parametrization of quasiperiodic LI-classes. J. Phys. A 30 (1997), no. 9, 3029-3056.
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LINKS
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Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
T. Ward, Exactly realizable sequences
Michael Baake, John A.G. Roberts, Alfred Weiss, Periodic orbits of linear endomorphisms on the 2-torus and its lattices, Aug 26, 2008. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 27 2008]
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FORMULA
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If b(n) is the n-th term of A001350, then the n-th term is (1/n)* Sum_{ d divides n }\mu(d)b(n/d)
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EXAMPLE
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a(7)=4 since the 7th term of A001350 is 29 and the first is 1, so there are (29-1)/7 = 4 orbits of length 7.
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PROGRAM
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(PARI) a(n)=if(n<3, n==1, sumdiv(n, d, moebius(n/d)*(fibonacci(d-1)+fibonacci(d+1)))/n)
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CROSSREFS
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Cf. A001350.
A006206(n)=a(n) except for n=2.
Sequence in context: A017910 A013979 A107458 this_sequence A006206 A095719 A153952
Adjacent sequences: A060277 A060278 A060279 this_sequence A060281 A060282 A060283
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KEYWORD
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easy,nonn
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AUTHOR
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Thomas Ward (t.ward(AT)uea.ac.uk), Mar 29 2001
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EXTENSIONS
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Replaced arXiv URL by the stable, non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2009
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