A080004 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={-1,2}.

1, 1, 1, 2, 4, 9, 15, 25, 46, 84, 156, 280, 501, 909, 1647, 2990, 5408, 9773, 17695, 32033, 58000, 104976, 189968, 343860, 622409, 1126617, 2039201, 3690898, 6680644, 12092173, 21887215, 39616409, 71706406, 129790404, 234923948

Offset: 0

Author

Vladimir Baltic, Feb 10 2003

Keywords

• nonn

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
• K. Edwards and M. A. Allen, Strongly restricted permutations and tiling with fences, Discrete Applied Mathematics, Volume 187, 31 May 2015, Pages 82-90.
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,4,-1,1,0,-1,-1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{1,0,1,1,4,-1,1,0,-1,-1},{1,1,1,2,4,9,15,25,46,84},40] (* Harvey P. Dale, Jun 18 2013 *)

Formula

a(n) = a(n-1)+a(n-3)+a(n-4)+4*a(n-5)-a(n-6)+a(n-7)-a(n-9)-a(n-10).

G.f.: -(x^5-1)/(x^10+x^9-x^7+x^6-4*x^5-x^4-x^3-x+1).