A080010 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, 9, 19, 38, 84, 193, 430, 940, 2074, 4609, 10223, 22611, 50022, 110780, 245348, 543189, 1202511, 2662417, 5894961, 13051820, 28897016, 63979205, 141653762, 313629217, 694390210, 1537413824, 3403913006, 7536438344

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..30.

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

Formula

Recurrence: a(n) = a(n-1)+a(n-2)+2*a(n-3)+3*a(n-4)+3*a(n-5)-2*a(n-6)-a(n-7)-a(n-10).

G.f.: -(x^5+x^3+x^2-1)/(x^10+x^7+2*x^6-3*x^5-3*x^4-2*x^3-x^2-x+1).

Prog

(PARI) Vec((1-x^2-x^3-x^5)/(1-x-x^2-2*x^3-3*x^4-3*x^5+2*x^6+x^7+x^10)+O(x^99)) \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

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

Sequence in context: A300445 A115238 A005994 * A135117 A038163 A327381

Adjacent sequences: A080007 A080008 A080009 * A080011 A080012 A080013

Keyword

nonn,easy

Author

Vladimir Baltic, Feb 10 2003

Status

approved