A079965 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={0,3}.

1, 0, 1, 1, 1, 3, 3, 5, 8, 10, 17, 24, 35, 54, 77, 116, 172, 252, 377, 555, 822, 1220, 1801, 2671, 3953, 5849, 8666, 12823, 18987, 28113, 41612, 61615, 91214, 135037, 199929, 295976, 438193, 648734, 960420, 1421893, 2105059, 3116482, 4613879, 6830695

Offset: 0

Author

Vladimir Baltic, Feb 19 2003

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into elements of the set {2,3,5,6}.

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

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{0,1,1,0,1,1},{1,0,1,1,1,3},50] (* Harvey P. Dale, Jul 10 2017 *)

Formula

a(n) = a(n-2)+a(n-3)+a(n-5)+a(n-6).

G.f.: -1/(x^6+x^5+x^3+x^2-1).