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A080002
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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=2, r=3, I={-1,0,1}.
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0
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1, 0, 0, 0, 1, 1, 0, 0, 1, 3, 1, 1, 1, 6, 6, 4, 5, 10, 20, 16, 20, 25, 50, 60, 66, 85, 125, 190, 216, 281, 365, 545, 701, 883, 1156, 1576, 2176, 2761, 3636, 4784, 6560, 8620, 11265, 14856, 19840, 26600, 34825, 46045, 60856, 81420, 107625, 142055, 187881, 249461
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OFFSET
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0,10
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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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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,2,-1,-1,0,0,-1).
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FORMULA
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Recurrence: a(n) = a(n-2)+a(n-4)+2*a(n-5)-a(n-6)-a(n-7)-a(n-10).
G.f.: (1-x^2-x^5)/(x^10+x^7+x^6-2*x^5-x^4-x^2+1).
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MATHEMATICA
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LinearRecurrence[{0, 1, 0, 1, 2, -1, -1, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 0, 0, 1, 3}, 60] (* Harvey P. Dale, Dec 14 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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