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Search: id:A079994
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| A079994 |
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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={0,1}. |
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+0
1
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| 1, 0, 0, 1, 3, 9, 13, 25, 59, 147, 328, 690, 1478, 3285, 7357, 16249, 35561, 77974, 171891, 379401, 835954, 1839288, 4047688, 8914186, 19636159, 43244340, 95216488, 209653186, 461673635, 1016681969, 2238835524, 4929989552
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OFFSET
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0,5
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COMMENT
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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={-1,0}.
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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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FORMULA
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Recurrence: a(n) = 2*a(n-2)+2*a(n-3)+4*a(n-4)+9*a(n-5)+10*a(n-6)-3*a(n-7)-9*a(n-8)-a(n-10)-12*a(n-11)-11*a(n-12)+a(n-13)+4*a(n-14)-a(n-15)+2*a(n-18)-a(n-20) G.f.: -(x^14-2*x^12-x^11-x^10+2*x^9-3*x^8+5*x^6+2*x^5+x^4+x^3+2*x^2-1)/(x^20-2*x^18+x^15-4*x^14-x^13+11*x^12+12*x^11+x^10+9*x^8+3*x^7-10*x^6-9*x^5-4*x^4-2*x^3-2*x^2+1)
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CROSSREFS
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Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Sequence in context: A106402 A125706 A113510 this_sequence A124825 A074938 A057260
Adjacent sequences: A079991 A079992 A079993 this_sequence A079995 A079996 A079997
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KEYWORD
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nonn
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AUTHOR
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Vladimir Baltic (baltic(AT)galeb.etf.bg.ac.yu), Feb 17 2003
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