A079957 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={0,1,3}.

1, 0, 0, 1, 0, 1, 2, 0, 2, 3, 1, 5, 5, 3, 10, 9, 9, 20, 17, 22, 39, 35, 51, 76, 74, 112, 150, 160, 239, 300, 346, 501, 610, 745, 1040, 1256, 1592, 2151, 2611, 3377, 4447, 5459, 7120, 9209, 11447, 14944, 19115, 24026, 31273, 39771, 50417, 65332, 82912, 105716

Offset: 0

Author

Vladimir Baltic, Feb 19 2003

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into elements of the set {3,5,6}.

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

Crossrefs

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

Formula

a(n) = a(n-3)+a(n-5)+a(n-6).

G.f.: -1/(x^6+x^5+x^3-1).