A080005 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={-1,1}.

1, 1, 1, 2, 4, 7, 11, 19, 35, 62, 107, 186, 328, 578, 1012, 1771, 3107, 5455, 9568, 16774, 29417, 51603, 90513, 158741, 278404, 488301, 856448, 1502116, 2634532, 4620700, 8104269, 14214069, 24929981, 43724610, 76688540, 134503903, 235906039

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..36.

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

K. Edwards, M. A. Allen, Strongly restricted permutations and tiling with fences, Discrete Applied Mathematics, Volume 187, 31 May 2015, Pages 82-90.

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

Formula

a(n) = a(n-1) + a(n-2) + a(n-4) + a(n-5) - 2*a(n-6) + a(n-8) - a(n-10), n>9.

G.f.: -(x^5+x^2-1)/(x^10-x^8+2*x^6-x^5-x^4-x^2-x+1).

Mathematica

CoefficientList[Series[-(x^5 + x^2 - 1)/(x^10 - x^8 + 2*x^6 - x^5 - x^4 - x^2 - x + 1), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jan 02 2017 *)

Crossrefs

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

Sequence in context: A000802 A236392 A200377 * A364590 A151992 A242362

Adjacent sequences: A080002 A080003 A080004 * A080006 A080007 A080008

Keyword

nonn

Author

Vladimir Baltic, Feb 10 2003

Status

approved