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Search: id:A079983
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| A079983 |
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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={-2,1,2}. |
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+0
1
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| 1, 1, 1, 1, 3, 6, 12, 20, 35, 60, 114, 207, 375, 671, 1213, 2180, 3954, 7139, 12892, 23250, 41996, 75793, 136891, 247133, 446211, 805505, 1454390, 2625744, 4740788, 8559108, 15453182, 27899503, 50371415, 90942627, 164192549, 296440115
(list; graph; listen)
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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,-1,2}.
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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)+a(n-3)-a(n-5)+4*a(n-6)-4*a(n-7)-3*a(n-8)-3*a(n-9)+3*a(n-10)+3*a(n-11)-5*a(n-12)+4*a(n-13)+4*a(n-14)+a(n-15)-2*a(n-16)-a(n-17)+a(n-18)-a(n-19)-a(n-20) G.f.: -(x^2-1)*(x^12+2*x^9-x^6-2*x^3+1)/(x^20+x^19-x^18+x^17+2*x^16-x^15-4*x^14-4*x^13+5*x^12-3*x^11-3*x^10+3*x^9+3*x^8+4*x^7-4*x^6+x^5-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: A096220 A034333 A006128 this_sequence A028926 A038577 A028925
Adjacent sequences: A079980 A079981 A079982 this_sequence A079984 A079985 A079986
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KEYWORD
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nonn
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AUTHOR
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Vladimir Baltic (baltic(AT)galeb.etf.bg.ac.yu), Feb 17 2003
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