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A079985
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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={-1,0,1}.
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0
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1, 0, 0, 0, 1, 2, 4, 0, 4, 10, 29, 40, 64, 88, 221, 420, 800, 1280, 2336, 4260, 8325, 15000, 27200, 48360, 89541, 164430, 303300, 549120, 1001156, 1824342, 3350169, 6122640, 11189504, 20391280, 37266329, 68097480, 124548224, 227452928, 415474816
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OFFSET
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0,6
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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 (1, 1, -1, 3, 2, 2, -6, -2, 2, -3, -1, -1, 1, 1).
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FORMULA
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a(n) = a(n-1) +a(n-2) -a(n-3) +3*a(n-4) +2*a(n-5) +2*a(n-6) -6*a(n-7) -2*a(n-8) +2*a(n-9) -3*a(n-10) -a(n-11) -a(n-12) +a(n-13) +a(n-14)
G.f.: -(x^8+x^7-x^6-x^5-2*x^4+x^3-x^2-x+1)/(x^14 +x^13 -x^12 -x^11 -3*x^10 +2*x^9 -2*x^8 -6*x^7 +2*x^6 +2*x^5 +3*x^4 -x^3 +x^2 +x-1)
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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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