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 A049864 a(n) = Sum_{k=0,1,2,...,n-4,n-2,n-1} a(k); a(n-3) is not a summand; 3 initial terms required. 11
 1, 1, 1, 2, 4, 8, 15, 28, 52, 97, 181, 338, 631, 1178, 2199, 4105, 7663, 14305, 26704, 49850, 93058, 173717, 324288, 605368, 1130077, 2109583, 3938086, 7351463, 13723420, 25618337, 47823297, 89274637, 166654357, 311103754, 580756168, 1084132616 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Number of binary sequences of length n-2 with no subsequence 0110. E.g., a(7)=28 because among the 32 (=2^5) binary sequences of length 5 only 01100,01101,00110 and 10110 contain the subsequence 0110. - Emeric Deutsch, May 04 2006 This is a_3(n) in the Doroslovacki reference. - Max Alekseyev, Jun 26 2007 Column 0 of A118890. - Emeric Deutsch, May 04 2006 LINKS R. Doroslovacki, Binary sequences without 011...110 (k-1 1's) for fixed k, Mat. Vesnik 46 (1994), no. 3-4, 93-98. Index entries for linear recurrences with constant coefficients, signature (2,0,-1,1). FORMULA a(n) = 2*a(n-1) - a(n-3) + a(n-4); 4 initial terms required. G.f.: (1+z)*(1-z)^2/(1 - 2z + z^3 - z^4). - Emeric Deutsch, May 04 2006 MAPLE (With a different offset:) a[0]:=1:a[1]:=2:a[2]:=4:a[3]:=8: for n from 4 to 35 do a[n]:=2*a[n-1]-a[n-3]+a[n-4] od: seq(a[n], n=0..35); # Emeric Deutsch, May 04 2006 MATHEMATICA LinearRecurrence[{2, 0, -1, 1}, {1, 1, 1, 2}, 40] (* Harvey P. Dale, Sep 24 2013 *) CROSSREFS Cf. A005251, A049858, A118890, A118891, A118892. Sequence in context: A008937 A128805 A141018 * A239554 A268393 A118870 Adjacent sequences:  A049861 A049862 A049863 * A049865 A049866 A049867 KEYWORD nonn AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Nov 16 2007, at the suggestion of Max Alekseyev STATUS approved

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Last modified January 23 16:29 EST 2022. Contains 350514 sequences. (Running on oeis4.)