A079974 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=4, I={0,2}.

1, 0, 1, 0, 2, 1, 3, 2, 5, 5, 9, 10, 16, 20, 30, 39, 56, 75, 106, 144, 201, 275, 382, 525, 727, 1001, 1384, 1908, 2636, 3636, 5021, 6928, 9565, 13200, 18222, 25149, 34715, 47914, 66137, 91285, 126001, 173914, 240052, 331336, 457338, 631251, 871304, 1202639

Offset

0,5

Comments

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

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

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

Recurrence: a(n) = a(n-2)+a(n-4)+a(n-5).

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

Mathematica

a=b=c=d=0; Table[e=a-d+1; a=b; b=c; c=d; d=e, {n, 25}] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011*)
LinearRecurrence[{0, 1, 0, 1, 1}, {1, 0, 1, 0, 2}, 50] (* Harvey P. Dale, Apr 12 2014 *)

Crossrefs

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

Sequence in context: A035579 A045931 A325193 * A102517 A062951 A263150

Adjacent sequences: A079971 A079972 A079973 * A079975 A079976 A079977

Keyword

nonn,easy

Author

Vladimir Baltic, Feb 17 2003

Status

approved