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A079995
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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={2}.
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0
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1, 1, 2, 4, 14, 39, 103, 255, 665, 1741, 4605, 12046, 31474, 82206, 215157, 563083, 1473635, 3855111, 10085589, 26386595, 69038554, 180630858, 472594580, 1236463719, 3235013481, 8463923170, 22144596592, 57937977232, 151585883920
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OFFSET
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0,3
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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}.
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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, 2, 3, 4, 6, 13, -9, -11, -7, 5, -1, -11, 3, 9, 4, -4, -1, 2, -1, -1).
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FORMULA
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a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +4*a(n-4) +6*a(n-5) +13*a(n-6) -9*a(n-7) -11*a(n-8) -7*a(n-9) +5*a(n-10) -a(n-11) -11*a(n-12) +3*a(n-13) +9*a(n-14) +4*a(n-15) -4*a(n-16) -a(n-17) +2*a(n-18) -a(n-19) -a(n-20).
G.f.: -(x^14 -x^12 +x^11 -x^10 -x^9 -x^8 +3*x^6 -x^5 +x^4 +3*x^3 +x^2-1)/ (x^20 +x^19 -2*x^18 +x^17 +4*x^16 -4*x^15 -9*x^14 -3*x^13 +11*x^12 +x^11 -5*x^10 +7*x^9 +11*x^8 +9*x^7 -13*x^6 -6*x^5 -4*x^4 -3*x^3 -2*x^2 -x+1)
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MATHEMATICA
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CoefficientList[Series[-(x^14-x^12+x^11-x^10-x^9-x^8+3x^6-x^5+ x^4+ 3x^3+ x^2-1)/ (x^20+ x^19-2x^18+ x^17+4x^16-4x^15-9x^14- 3x^13+ 11x^12+ x^11- 5x^10+ 7x^9+11x^8+9x^7-13x^6-6x^5-4x^4-3x^3-2x^2-x+1), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 2, 3, 4, 6, 13, -9, -11, -7, 5, -1, -11, 3, 9, 4, -4, -1, 2, -1, -1}, {1, 1, 2, 4, 14, 39, 103, 255, 665, 1741, 4605, 12046, 31474, 82206, 215157, 563083, 1473635, 3855111, 10085589, 26386595}, 40] (* Harvey P. Dale, Oct 29 2017 *)
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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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