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 A005674 a(n) = 2^(n-1) + 2^[ n/2 ] + 2^[ (n-1)/2 ] - F(n+3). (Formerly M2837) 3
 0, 0, 0, 0, 1, 3, 10, 25, 63, 144, 327, 711, 1534, 3237, 6787, 14056, 28971, 59283, 120894, 245457, 497167, 1004256, 2025199, 4077007, 8198334, 16467597, 33052491, 66293208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS a(n) is the number of compositions of n where mixing of even and odd summands occurs. That is, at least one even summand is bracketed by two odd summands, or vice versa. - Gregory L. Simay, Jul 27 2016 REFERENCES R. K. Guy, personal communication. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS R. K. Guy, Letter to N. J. A. Sloane, 1987 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. FORMULA From Gregory L. Simay, Jul 27 2016: (Start) If n=2k, then a(n) = 2^(n-1) - 2*A079289(n) + 2^(n/2 - 1) + F(n). If n=2k-1, then a(n) = 2^(n-1) - 2*A079289(n) + F(n). (End) EXAMPLE a(6) = a(2*3) = 2^5 - f(9) + 3*2^2 = 32 - 34 + 12 = 10. The 10 compositions are (1,4,1), (3,2,1), (1,2,3), (2,1,2,1), (1,2,1,2), (2,1,1,2), (1,2,2,1), (1,2,1,1,1), (1,1,2,1,1), (1,1,1,2,1). MAPLE A005674:=-z**4/(2*z-1)/(z**2+z-1)/(-1+2*z**2); # [Conjectured by Simon Plouffe in his 1992 dissertation.] CROSSREFS Cf. A079289, A027558 divided by 2. Sequence in context: A067988 A297186 A262380 * A089100 A089117 A176610 Adjacent sequences:  A005671 A005672 A005673 * A005675 A005676 A005677 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 22 09:14 EST 2020. Contains 332133 sequences. (Running on oeis4.)