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Search: id:A079988
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| A079988 |
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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={0,1,2}. |
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+0
1
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| 1, 0, 0, 0, 1, 3, 3, 3, 6, 10, 29, 39, 61, 101, 179, 335, 566, 928, 1575, 2705, 4747, 8117, 13782, 23464, 40216, 69209, 118650, 202712, 346508, 593180, 1016874, 1741871, 2981190, 5101520, 8733466, 14956519, 25611753, 43847283, 75061015, 128505176
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OFFSET
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0,6
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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,-1,0}.
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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-2)+a(n-3)+a(n-4)+4*a(n-5)+4*a(n-6)-a(n-7)-3*a(n-8)-2*a(n-9)+a(n-10)-4*a(n-11)-3*a(n-12)+a(n-13)+4*a(n-14)-a(n-16)+a(n-17)+a(n-18)-a(n-20) G.f.: -(x^14-x^12-x^11+x^9-2*x^8+2*x^6+x^5+x^3+x^2-1)/(x^20-x^18-x^17+x^16-4*x^14-x^13+3*x^12+4*x^11-x^10+2*x^9+3*x^8+x^7-4*x^6-4*x^5-x^4-x^3-x^2+1)
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CROSSREFS
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Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Adjacent sequences: A079985 A079986 A079987 this_sequence A079989 A079990 A079991
Sequence in context: A132972 A113920 A081848 this_sequence A061021 A143015 A126608
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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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