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Search: id:A079989
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| A079989 |
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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={1,2}. |
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+0
1
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| 1, 1, 1, 1, 5, 13, 27, 51, 103, 221, 498, 1064, 2240, 4728, 10076, 21559, 46075, 98085, 208759, 444727, 948151, 2021335, 4307861, 9179111, 19560273, 41686260, 88842852, 189337896, 403497908, 859893060, 1832537757, 3905386173
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OFFSET
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0,5
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COMMENT
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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}.
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REFERENCES
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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
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Recurrence: a(n) = a(n-1)+a(n-2)+2*a(n-3)+a(n-4)+3*a(n-5)+4*a(n-6)-7*a(n-7)-7*a(n-8)-6*a(n-9)+6*a(n-10)-2*a(n-11)-a(n-12)+a(n-13)+4*a(n-14)+a(n-15)-3*a(n-16)+a(n-18)-a(n-19)-a(n-20) G.f.: -(x^14-x^12+x^11-x^9-x^8+x^6-x^5+3*x^3+x^2-1)/(x^20+x^19-x^18+3*x^16-x^15-4*x^14-x^13+x^12+2*x^11-6*x^10+6*x^9+7*x^8+7*x^7-4*x^6-3*x^5-x^4-2*x^3-x^2-x+1)
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CROSSREFS
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Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Sequence in context: A025193 A002717 A023541 this_sequence A062480 A027024 A055328
Adjacent sequences: A079986 A079987 A079988 this_sequence A079990 A079991 A079992
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KEYWORD
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nonn
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AUTHOR
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Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Feb 17 2003
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