A079956 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={0,1,4}.

1, 0, 0, 1, 1, 0, 2, 2, 1, 3, 5, 3, 6, 10, 9, 12, 21, 22, 27, 43, 52, 61, 91, 117, 140, 195, 260, 318, 426, 572, 718, 939, 1258, 1608, 2083, 2769, 3584, 4630, 6110, 7961, 10297, 13509, 17655, 22888, 29916, 39125, 50840, 66313, 86696, 112853, 147069, 192134

Offset: 0

Author

Vladimir Baltic, Feb 19 2003

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into elements of the set {3,4,6}.

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 (0,0,1,1,0,1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{0,0,1,1,0,1},{1,0,0,1,1,0},60] (* Harvey P. Dale, Oct 05 2016 *)

Formula

a(n) = a(n-3)+a(n-4)+a(n-6).

G.f.: -1/(x^6+x^4+x^3-1).