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A080004
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}.
0
1, 1, 1, 2, 4, 9, 15, 25, 46, 84, 156, 280, 501, 909, 1647, 2990, 5408, 9773, 17695, 32033, 58000, 104976, 189968, 343860, 622409, 1126617, 2039201, 3690898, 6680644, 12092173, 21887215, 39616409, 71706406, 129790404, 234923948
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
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 and M. A. Allen, Strongly restricted permutations and tiling with fences, Discrete Applied Mathematics, Volume 187, 31 May 2015, Pages 82-90.
FORMULA
a(n) = a(n-1)+a(n-3)+a(n-4)+4*a(n-5)-a(n-6)+a(n-7)-a(n-9)-a(n-10).
G.f.: -(x^5-1)/(x^10+x^9-x^7+x^6-4*x^5-x^4-x^3-x+1).
MATHEMATICA
LinearRecurrence[{1, 0, 1, 1, 4, -1, 1, 0, -1, -1}, {1, 1, 1, 2, 4, 9, 15, 25, 46, 84}, 40] (* Harvey P. Dale, Jun 18 2013 *)
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Feb 10 2003
STATUS
approved