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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
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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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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={-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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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 2, 2, 4, 9, 10, -3, -9, 0, -1, -12, -11, 1, 4, -1, 0, 0, 2, 0, -1).
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FORMULA
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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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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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