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A006979
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a(n)=number of compositions of n in which the maximum part size is 5.
(Formerly M1410)
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1
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0, 0, 0, 0, 0, 1, 2, 5, 12, 28, 63, 139, 303, 653, 1394, 2953, 6215, 13008, 27095, 56201, 116143, 239231, 491326, 1006420, 2056633, 4193706, 8534653, 17337764, 35162804, 71205504, 143990366, 290795624, 586566102, 1181834852, 2378701408
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,7
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COMMENTS
| a(n) is also the number of binary sequences of length n-1 in which the longest run of 0's is exactly 4. Example: a(7) = 5 because there are 5 binary sequences of length 6 in which the longest run of 0's is exactly 4: 000010, 000011, 010000, 110000, 100001. - Geoffrey Critzer, Nov 07 2008
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. L. Yucas, Counting special sets of binary Lyndon words, Ars Combin., 31 (1991), 21-29.
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FORMULA
| G.f.: x^5 / ((1-x-x^2-x^3-x^4) * (1-x-x^2-x^3-x^4-x^5)). - Alois P. Heinz, Oct 29 2008
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MAPLE
| a:= n-> (Matrix(9, (i, j)-> if i=j-1 then 1 elif j=1 then [2, 1, 0, -1, -3, -4, -3, -2, -1][i] else 0 fi)^n) [1, 6]: seq (a(n), n=5..40); # Alois P. Heinz, Oct 29 2008
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CROSSREFS
| Cf. A048003.
Sequence in context: A118898 A111586 A192657 * A019301 A006980 A045623
Adjacent sequences: A006976 A006977 A006978 * A006980 A006981 A006982
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms and better definition from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2008
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