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A079984
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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={-1,1,2}.
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0
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1, 1, 1, 1, 2, 5, 10, 16, 26, 43, 80, 148, 264, 465, 816, 1444, 2588, 4619, 8214, 14591, 25903, 46071, 82015, 145904, 259492, 461408, 820468, 1459332, 2595687, 4616613, 8210719, 14602409, 25970414, 46189613, 82149988, 146106304, 259853016
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OFFSET
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0,5
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COMMENTS
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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,-1,1}.
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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, -1, 1, 3, -4, -4, -2, 4, 2, -4, 4, 3, -1, -1, -1, 1, -1, -1).
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FORMULA
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a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) +a(n-5) +3*a(n-6) -4*a(n-7) -4*a(n-8) -2*a(n-9) +4*a(n-10) +2*a(n-11) -4*a(n-12) +4*a(n-13) +3*a(n-14) -a(n-15) -a(n-16) -a(n-17) +a(n-18) -a(n-19) -a(n-20)
G.f.: -(x^14-x^12+2*x^11-x^9-x^8+x^6-x^5+2*x^3+x^2-1)/((x^19 -x^17 +2*x^16 -x^15 +2*x^14 -5*x^13 +x^12 +3*x^11 -5*x^10 +x^9 +x^8 +3*x^7 +x^6 -4*x^5 +3*x^4 -2*x^3 +x^2 -2*x+1) *(x+1))
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MATHEMATICA
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CoefficientList[Series[-(x^14-x^12+2x^11-x^9-x^8+x^6-x^5+2x^3+x^2-1)/ ((x^19-x^17+2x^16x^15+2x^14-5x^13+x^12+3x^11-5x^10+x^9+x^8+ 3x^7+x^6- 4x^5+ 3x^4- 2x^3+ x^2-2x+1)(x+1)), {x, 0, 40}], x] (* or *) LinearRecurrence[ {1, 1, 1, -1, 1, 3, -4, -4, -2, 4, 2, -4, 4, 3, -1, -1, -1, 1, -1, -1}, {1, 1, 1, 1, 2, 5, 10, 16, 26, 43, 80, 148, 264, 465, 816, 1444, 2588, 4619, 8214, 14591}, 50] (* Harvey P. Dale, Feb 07 2015 *)
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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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