A079999 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=3, I={0,1,2}.

1, 0, 0, 0, 1, 1, 1, 1, 1, 4, 4, 5, 7, 10, 16, 22, 29, 40, 60, 84, 118, 165, 230, 330, 466, 653, 919, 1297, 1831, 2585, 3640, 5124, 7233, 10201, 14380, 20272, 28572, 40289, 56816, 80096, 112912, 159196, 224449, 316456, 446164, 629004, 886821, 1250329, 1762801

Offset

0,10

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..48.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 1, 2, 1, 0, -1, 0, -1).

Formula

Recurrence: a(n) = a(n-3)+a(n-4)+2*a(n-5)+a(n-6)-a(n-8)-a(n-10)

G.f.: -(x^5+x^3-1)/(x^10+x^8-x^6-2*x^5-x^4-x^3+1)

Mathematica

LinearRecurrence[{0, 0, 1, 1, 2, 1, 0, -1, 0, -1}, {1, 0, 0, 0, 1, 1, 1, 1, 1, 4}, 50] (* Harvey P. Dale, Dec 12 2024 *)

Crossrefs

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

Sequence in context: A091349 A103483 A170934 * A058619 A198999 A095945

Adjacent sequences: A079996 A079997 A079998 * A080000 A080001 A080002

Keyword

nonn

Author

Vladimir Baltic, Feb 10 2003

Status

approved