

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
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OFFSET

0,7


COMMENTS

a(n) is also the number of binary sequences of length n1 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), 2129.


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 / ((1xx^2x^3x^4)*(1xx^2x^3x^4x^5)).  Alois P. Heinz, Oct 29 2008


MAPLE

a:= n> (Matrix(9, (i, j)> if i=j1 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

Simon Plouffe


EXTENSIONS

More terms and better definition from Alois P. Heinz, Oct 29 2008
Offset corrected by Matthew House, Feb 11 2017


STATUS

approved



