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A079967
Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={4}.
0
1, 1, 2, 4, 8, 15, 30, 58, 113, 220, 429, 835, 1627, 3169, 6173, 12024, 23422, 45623, 88869, 173107, 337194, 656817, 1279409, 2492150, 4854439, 9455922, 18419114, 35878442, 69887326, 136132954, 265172275, 516526919, 1006138588, 1959849178
OFFSET
0,3
COMMENTS
Number of compositions (ordered partitions) of n into elements of the set {1,2,3,4,6}.
Note that the number of compositions of n with parts in N which avoid the pattern 221 (see Heubach/Mansour) is not this sequence but A134044.
REFERENCES
D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.
LINKS
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135.
S. Heubach and T. Mansour, Enumeration of 3-letter patterns in combinations, arXiv:math/0603285 [math.CO], 2006.
FORMULA
a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-6).
G.f.: -1/(x^6+x^4+x^3+x^2+x-1).
KEYWORD
nonn,easy
AUTHOR
Vladimir Baltic, Feb 19 2003
STATUS
approved