A080014 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=2, I={1}.

1, 1, 1, 3, 6, 10, 18, 35, 65, 119, 221, 412, 764, 1416, 2629, 4881, 9057, 16807, 31194, 57894, 107442, 199399, 370065, 686799, 1274617, 2365544, 4390184, 8147680, 15121161, 28063153, 52082017, 96658283, 179386750, 332921362, 617864098

Offset: 0

Author

Vladimir Baltic, Jan 24 2003

Keywords

• nonn
• easy

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 (1,1,1,1,-1,-1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{1,1,1,1,-1,-1},{1,1,1,3,6,10},40] (* Harvey P. Dale, Mar 10 2024 *)

PARI

Vec(-(x^2-1)/(x^6+x^5-x^4-x^3-x^2-x+1)+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Formula

Recurrence: a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6).

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