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 A006979 a(n) is the number of compositions of n in which the maximum part size is 5. (Formerly M1410) 2
 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; text; internal format)
 OFFSET 0,7 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 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. LINKS Matthew House, Table of n, a(n) for n = 0..3390 Index entries for linear recurrences with constant coefficients, signature (2,1,0,-1,-3,-4,-3,-2,-1). 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 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 MATHEMATICA CoefficientList[Series[x^5/((1 - x - x^2 - x^3 - x^4) (1 - x - x^2 - x^3 - x^4 - x^5)), {x, 0, 34}], x] (* Michael De Vlieger, Feb 11 2017 *) CROSSREFS Cf. A048003. Sequence in context: A111586 A192657 A320590 * A019301 A006980 A045623 Adjacent sequences:  A006976 A006977 A006978 * A006980 A006981 A006982 KEYWORD nonn AUTHOR EXTENSIONS More terms and better definition from Alois P. Heinz, Oct 29 2008 Offset corrected by Matthew House, Feb 11 2017 STATUS approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)