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 A007039 Number of cyclic binary n-bit strings with no alternating substring of length >2. (Formerly M0241) 3
 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; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS John W. Layman observes that the second differences give the sequence shifted to the right. REFERENCES 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). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1000 Index to sequences with linear recurrences with constant coefficients, signature (2,-1,0,1). FORMULA 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] MATHEMATICA 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 *) CROSSREFS Cf. A007040. Sequence in context: A186507 A032306 A058756 * A025248 A213170 A101416 Adjacent sequences:  A007036 A007037 A007038 * A007040 A007041 A007042 KEYWORD nonn,easy,eigen AUTHOR STATUS approved

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