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A080012
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={0}.
1
1, 0, 1, 2, 6, 11, 23, 51, 113, 244, 526, 1142, 2483, 5389, 11687, 25358, 55034, 119430, 259151, 562340, 1220276, 2647993, 5746085, 12468857, 27057165, 58713537, 127407187, 276470942, 599936262, 1301849496, 2824986880, 6130163753
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
FORMULA
a(n) = 2a(n-2)+3a(n-3)+4a(n-4)+5a(n-5)+a(n-6)-2a(n-7)-a(n-8)-a(n-9)-a(n-10).
G.f.: -(x^5+x^3+x^2-1)/(x^10+x^9+x^8+2*x^7-x^6-5*x^5-4*x^4-3*x^3-2*x^2+1)
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Feb 10 2003
STATUS
approved