A079991 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-1,1}.

1, 1, 1, 2, 5, 13, 29, 58, 124, 280, 632, 1406, 3101, 6851, 15217, 33846, 75181, 166823, 370177, 821760, 1824620, 4051056, 8993220, 19964240, 44320545, 98393849, 218438981, 484939834, 1076573833, 2390015565, 5305896445, 11779231650

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..31.

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

Formula

a(n) = 2*a(n-1) +3*a(n-4) +a(n-6) -8*a(n-7) -a(n-8) -3*a(n-10) +2*a(n-13) +a(n-14).

G.f.: -(x^8+x^7-x^6-2*x^4-x^2-x+1)/(x^14+2*x^13-3*x^10-x^8-8*x^7+x^6+3*x^4+2*x-1).

Crossrefs

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

Sequence in context: A050950 A259678 A218152 * A091270 A214633 A282831

Adjacent sequences: A079988 A079989 A079990 * A079992 A079993 A079994

Keyword

nonn,easy

Author

Vladimir Baltic, Feb 17 2003

Status

approved