A080002 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={-1,0,1}.

1, 0, 0, 0, 1, 1, 0, 0, 1, 3, 1, 1, 1, 6, 6, 4, 5, 10, 20, 16, 20, 25, 50, 60, 66, 85, 125, 190, 216, 281, 365, 545, 701, 883, 1156, 1576, 2176, 2761, 3636, 4784, 6560, 8620, 11265, 14856, 19840, 26600, 34825, 46045, 60856, 81420, 107625, 142055, 187881, 249461

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

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{0,1,0,1,2,-1,-1,0,0,-1},{1,0,0,0,1,1,0,0,1,3},60] (* Harvey P. Dale, Dec 14 2011 *)

Formula

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

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