cp's OEIS Frontend

A049864 a(n) = Sum_{k=0,1,2,...,n-4,n-2,n-1} a(k); a(n-3) is not a summand, with a(0)=a(1)=a(2)=1.

%I A049864 #33 Feb 04 2025 18:31:20
%S A049864 1,1,1,2,4,8,15,28,52,97,181,338,631,1178,2199,4105,7663,14305,26704,
%T A049864 49850,93058,173717,324288,605368,1130077,2109583,3938086,7351463,
%U A049864 13723420,25618337,47823297,89274637,166654357,311103754,580756168,1084132616,2023815835
%N A049864 a(n) = Sum_{k=0,1,2,...,n-4,n-2,n-1} a(k); a(n-3) is not a summand, with a(0)=a(1)=a(2)=1.
%C A049864 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
%C A049864 This is a_3(n) in the Doroslovacki reference. - _Max Alekseyev_, Jun 26 2007
%C A049864 Column 0 of A118890. - _Emeric Deutsch_, May 04 2006
%H A049864 R. Doroslovacki, <a href="https://www.emis.de/journals/MV/9434/7.html">Binary sequences without 011...110 (k-1 1's) for fixed k</a>, Mat. Vesnik 46 (1994), no. 3-4, 93-98.
%H A049864 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,1).
%F A049864 a(n) = 2*a(n-1) - a(n-3) + a(n-4).
%F A049864 G.f.: (1+z)*(1-z)^2/(1 - 2z + z^3 - z^4). - _Emeric Deutsch_, May 04 2006
%p A049864 (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
%t A049864 LinearRecurrence[{2,0,-1,1},{1,1,1,2},40] (* _Harvey P. Dale_, Sep 24 2013 *)
%Y A049864 Cf. A005251, A049858, A118890, A118891, A118892.
%K A049864 nonn,easy
%O A049864 0,4
%A A049864 _Clark Kimberling_
%E A049864 Edited by _N. J. A. Sloane_, Nov 16 2007, at the suggestion of _Max Alekseyev_