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A079987
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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={-1,0,2}.
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0
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1, 0, 0, 1, 2, 3, 5, 7, 15, 29, 49, 84, 149, 268, 484, 855, 1508, 2684, 4784, 8516, 15134, 26873, 47782, 85004, 151149, 268704, 477685, 849299, 1510163, 2685089, 4773851, 8487625, 15090786, 26831239, 47705352, 84818268, 150803857, 268125092
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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={-2,0,1}.
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REFERENCES
| 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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FORMULA
| Recurrence: a(n) = 2*a(n-1)-2*a(n-2)+3*a(n-3)-2*a(n-4)+4*a(n-5)-a(n-6)-2*a(n-7)+4*a(n-8)-5*a(n-9)+4*a(n-10)-6*a(n-11)+3*a(n-12)-2*a(n-14)+a(n-15)-2*a(n-16)+2*a(n-17)-a(n-18) G.f.: -(x^12-2*x^11+2*x^10-2*x^9+2*x^8-x^7-x^6+3*x^5-2*x^4+2*x^3-2*x^2+2*x-1)/(x^18-2*x^17+2*x^16-x^15+2*x^14-3*x^12+6*x^11-4*x^10+5*x^9-4*x^8+2*x^7+x^6-4*x^5+2*x^4-3*x^3+2*x^2-2*x+1)
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MATHEMATICA
| LinearRecurrence[{2, -2, 3, -2, 4, -1, -2, 4, -5, 4, -6, 3, 0, -2, 1, -2, 2, -1}, {1, 0, 0, 1, 2, 3, 5, 7, 15, 29, 49, 84, 149, 268, 484, 855, 1508, 2684}, 40] (* From Harvey P. Dale, Apr 29 2011 *)
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CROSSREFS
| Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Sequence in context: A157833 A175758 A151531 * A085547 A058702 A024377
Adjacent sequences: A079984 A079985 A079986 * A079988 A079989 A079990
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KEYWORD
| nonn
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AUTHOR
| Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Feb 17 2003
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