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A079984
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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={-1,1,2}.
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0
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1, 1, 1, 1, 2, 5, 10, 16, 26, 43, 80, 148, 264, 465, 816, 1444, 2588, 4619, 8214, 14591, 25903, 46071, 82015, 145904, 259492, 461408, 820468, 1459332, 2595687, 4616613, 8210719, 14602409, 25970414, 46189613, 82149988, 146106304, 259853016
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Also, 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={-2,-1,1}.
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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.
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FORMULA
| Recurrence: a(n) = a(n-1)+a(n-2)+a(n-3)-a(n-4)+a(n-5)+3*a(n-6)-4*a(n-7)-4*a(n-8)-2*a(n-9)+4*a(n-10)+2*a(n-11)-4*a(n-12)+4*a(n-13)+3*a(n-14)-a(n-15)-a(n-16)-a(n-17)+a(n-18)-a(n-19)-a(n-20) G.f.: -(x^14-x^12+2*x^11-x^9-x^8+x^6-x^5+2*x^3+x^2-1)/((x^19-x^17+2*x^16-x^15+2*x^14-5*x^13+x^12+3*x^11-5*x^10+x^9+x^8+3*x^7+x^6-4*x^5+3*x^4-2*x^3+x^2-2*x+1)*(x+1))
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CROSSREFS
| Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Sequence in context: A078435 A049815 A047992 * A027613 A192701 A067112
Adjacent sequences: A079981 A079982 A079983 * A079985 A079986 A079987
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KEYWORD
| nonn
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AUTHOR
| Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Feb 17 2003
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