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A049864
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a(n)=Sum{a(k): k=0,1,2,...,n-4,n-2,n-1}; a(n-3) is not a summand; 3 initial terms required.
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9
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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; internal format)
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OFFSET
| 0,4
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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 (deutsch(AT)duke.poly.edu), May 04 2006
This is a_3(n) in the Doroslovacki reference. - Max Alekseyev, Jun 26 2007
Column 0 of A118890. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 04 2006
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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 to sequences with linear recurrences with constant coefficients, signature (2,0,-1,1).
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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 (deutsch(AT)duke.poly.edu), May 04 2006
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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 (deutsch(AT)duke.poly.edu), May 04 2006
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CROSSREFS
| Cf. A005251, A049858, A118890, A118891, A118892.
Sequence in context: A008937 A128805 A141018 * A118870 A171857 A190160
Adjacent sequences: A049861 A049862 A049863 * A049865 A049866 A049867
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 16 2007, at the suggestion of Max Alekseyev.
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