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}.

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

Author

Vladimir Baltic, Feb 19 2003

Keywords

• nonn
• easy

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.
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,0,1).

Crossrefs

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

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).