A080003 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={1,2}.

1, 1, 1, 1, 4, 8, 13, 22, 40, 77, 140, 252, 456, 834, 1525, 2775, 5049, 9195, 16760, 30536, 55617, 101304, 184544, 336193, 612424, 1115600, 2032216, 3702000, 6743761, 12284729, 22378393, 40765513, 74260396, 135276192, 246425309

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

Crossrefs

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

Formula

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

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