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A080014
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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=2, I={1}.
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77
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1, 1, 1, 3, 6, 10, 18, 35, 65, 119, 221, 412, 764, 1416, 2629, 4881, 9057, 16807, 31194, 57894, 107442, 199399, 370065, 686799, 1274617, 2365544, 4390184, 8147680, 15121161, 28063153, 52082017, 96658283, 179386750, 332921362, 617864098
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OFFSET
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0,4
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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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FORMULA
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Recurrence: a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6).
G.f.: -(x^2-1)/(x^6+x^5-x^4-x^3-x^2-x+1).
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MATHEMATICA
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LinearRecurrence[{1, 1, 1, 1, -1, -1}, {1, 1, 1, 3, 6, 10}, 40] (* Harvey P. Dale, Mar 10 2024 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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