A080011 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}.

1, 1, 1, 3, 7, 15, 29, 59, 126, 262, 542, 1121, 2328, 4839, 10039, 20827, 43220, 89704, 186172, 386345, 801768, 1663916, 3453137, 7166272, 14872078, 30863935, 64051787, 132926308, 275861116, 572492846, 1188091024, 2465638247

Offset

0,4

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..31.

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 (1,1,1,2,3,-1,0,1,-1,-1).

Formula

a(n) = a(n-1)+a(n-2)+a(n-3)+2*a(n-4)+3*a(n-5)-a(n-6)+a(n-8)-a(n-9)-a(n-10).

G.f.: -(x^5+x^2-1)/(x^10+x^9-x^8+x^6-3*x^5-2*x^4-x^3-x^2-x+1)

Mathematica

LinearRecurrence[{1, 1, 1, 2, 3, -1, 0, 1, -1, -1}, {1, 1, 1, 3, 7, 15, 29, 59, 126, 262}, 40] (* Harvey P. Dale, Nov 03 2022 *)

Crossrefs

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

Sequence in context: A153823 A283007 A283258 * A284022 A327554 A120538

Adjacent sequences: A080008 A080009 A080010 * A080012 A080013 A080014

Keyword

nonn,changed

Author

Vladimir Baltic, Feb 10 2003

Status

approved