A080001 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={-1,0,2}.

1, 0, 0, 1, 1, 1, 1, 2, 4, 3, 4, 8, 10, 13, 16, 24, 36, 43, 59, 85, 115, 156, 207, 289, 401, 533, 729, 1002, 1368, 1864, 2526, 3465, 4740, 6436, 8785, 11995, 16375, 22331, 30420, 41550, 56705, 77296, 105456, 143874, 196321, 267792, 365216, 498356

Offset

0,8

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..47.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135

Formula

Recurrence: a(n) = a(n-3)+a(n-4)+2*a(n-5)-a(n-9)-a(n-10) G.f.: -(x^5-1)/(x^10+x^9-2*x^5-x^4-x^3+1)

Crossrefs

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

Sequence in context: A328486 A349606 A332224 * A178938 A228196 A261326

Adjacent sequences: A079998 A079999 A080000 * A080002 A080003 A080004

Keyword

nonn

Author

Vladimir Baltic, Feb 10 2003

Status

approved