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Search: id:A049864
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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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6
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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; listen)
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OFFSET
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0,4
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COMMENT
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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
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R. Doroslovacki, Binary sequences without 011...110 (k-1 1's) for fixed k, Mat. Vesnik 46 (1994), no. 3-4, 93-98.
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FORMULA
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a(n)=2*a(n-1)-a(n-3)+a(n-4); 4 initial terms required.
(With a different offset:) G.f.=(1+z^3)/(1-2z+z^3-z^4). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 04 2006
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MAPLE
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(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
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Cf. A005251, A049858, A118890, A118891, A118892.
Sequence in context: A073769 A008937 A128805 this_sequence A118870 A088532 A036621
Adjacent sequences: A049861 A049862 A049863 this_sequence A049865 A049866 A049867
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Edited by njas, Nov 16 2007, at the suggestion of Max Alekseyev.
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