A079968 - OEIS

A079968

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={3}.

1, 1, 2, 4, 7, 14, 27, 51, 98, 187, 357, 683, 1305, 2494, 4767, 9110, 17411, 33276, 63596, 121544, 232293, 443954, 848478, 1621597, 3099169, 5923081, 11320094, 21634776, 41348026, 79023662, 151028714, 288643577, 551650823, 1054305916

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OFFSET

0,3

COMMENTS

Number of compositions (ordered partitions) of n into elements of the set {1,2,3,5,6}.

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

Table of n, a(n) for n=0..33.

D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.

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

FORMULA

a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-5)+a(n-6).

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

MATHEMATICA

LinearRecurrence[{1, 1, 1, 0, 1, 1}, {1, 1, 2, 4, 7, 14}, 40] (* Harvey P. Dale, Jun 05 2013 *)

CROSSREFS

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