A079969 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={2}.

1, 1, 2, 3, 6, 11, 21, 38, 70, 128, 236, 434, 799, 1469, 2702, 4969, 9140, 16811, 30921, 56872, 104604, 192396, 353872, 650872, 1197141, 2201885, 4049898, 7448923, 13700706, 25199527, 46349157, 85249390, 156798074, 288396620, 530444084

Offset: 0

Author

Vladimir Baltic, Feb 19 2003

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into elements of the set {1,2,4,5,6}.

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

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{1,1,0,1,1,1},{1,1,2,3,6,11},40] (* Harvey P. Dale, Aug 03 2014 *)

Formula

a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-5)+a(n-6).

G.f.: -1/(x^6+x^5+x^4+x^2+x-1).