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Search: id:A005666
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| A005666 |
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Tower of Hanoi with cyclic moves only.
(Formerly M1755)
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+0
1
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| 0, 2, 7, 21, 59, 163, 447, 1223, 3343, 9135, 24959, 68191, 186303, 508991, 1390591, 3799167, 10379519, 28357375, 77473791, 211662335, 578272255, 1579869183, 4316282879
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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J.-P. Allouche, Note on the cyclic towers of Hanoi, Theoret. Comput. Sci., 123 (1994), 3-7.
M. D. Atkinson, The Cyclic Towers of Hanoi, Info. Proc. Letters, 13 (1981), 118-119.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 18.
D. G. Poole, The towers and triangles of Professor Claus (or, Pascal knows Hanoi), Math. Mag., 67 (1994), 323-344.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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.
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FORMULA
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a(n) = (1/(4*s3))*((1+s3)^(n+2)-(1-s3)^(n+2))-1 where s3 = sqrt(3).
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MAPLE
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A005666:=z*(2+z)/(z-1)/(2*z**2+2*z-1); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A005665.
Seems to be A28859(n)-1.
Sequence in context: A079034 A018036 A007050 this_sequence A159972 A106271 A027990
Adjacent sequences: A005663 A005664 A005665 this_sequence A005667 A005668 A005669
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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