A080009 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={2}.

1, 1, 2, 4, 11, 26, 56, 127, 288, 660, 1500, 3401, 7729, 17565, 39930, 90735, 206176, 468536, 1064750, 2419661, 5498621, 12495505, 28395889, 64529315, 146642077, 333242093, 757288191, 1720927502, 3910785158, 8887207808, 20196062308

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
• Index entries for linear recurrences with constant coefficients, signature (1,1,2,3,5,0,1,-1,-1,-1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{1,1,2,3,5,0,1,-1,-1,-1},{1,1,2,4,11,26,56,127,288,660},40] (* Harvey P. Dale, Nov 20 2021 *)

Formula

a(n) = a(n-1)+a(n-2)+2*a(n-3)+3*a(n-4)+5*a(n-5)+a(n-7)-a(n-8)-a(n-9)-a(n-10).

G.f.: -(x^5+x^3-1)/(x^10+x^9+x^8-x^7-5*x^5-3*x^4-2*x^3-x^2-x+1)