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A007039
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Number of cyclic binary n-bit strings with no alternating substring of length >2.
(Formerly M0241)
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3
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2, 2, 2, 6, 12, 20, 30, 46, 74, 122, 200, 324, 522, 842, 1362, 2206, 3572, 5780, 9350, 15126, 24474, 39602, 64080, 103684, 167762, 271442, 439202, 710646, 1149852, 1860500, 3010350, 4870846, 7881194, 12752042, 20633240, 33385284, 54018522
(list;
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OFFSET
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1,1
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COMMENTS
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John W. Layman observes that the second differences give the sequence shifted to the right.
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REFERENCES
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Z. Agur et al., The number of fixed points of the majority rule, Discr. Math., 70 (1988), 295-302.
Moser, W. O. J.; Cyclic binary strings without long runs of like (alternating) bits. Fibonacci Quart. 31 (1993), no. 1, 2-6.
A. McLeod and W. O. J. Moser, Counting cyclic binary strings, Math. Mag., 80 (No. 1, 2007), 29-37.
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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Vincenzo Librandi, Table of n, a(n) for n = 1000
Index to sequences with linear recurrences with constant coefficients, signature (2,-1,0,1).
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FORMULA
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For n >= 5, a(n) = 2a(n-1) - a(n-2) + a(n-4). (from David W. Wilson)
G.f.: 2*x*(1+x)*(1-2*x+2*x^2)/((1-x+x^2)*(1-x-x^2)). [Colin Barker, Mar 28 2012]
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MATHEMATICA
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CoefficientList[Series[2*(1+x)*(1-2*x+2*x^2)/((1-x+x^2)*(1-x-x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 16 2012 *)
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CROSSREFS
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Cf. A007040.
Sequence in context: A186507 A032306 A058756 * A025248 A213170 A101416
Adjacent sequences: A007036 A007037 A007038 * A007040 A007041 A007042
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KEYWORD
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nonn,easy,eigen
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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