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A166871
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Permutation of the integers: 3 positives, 2 negatives.
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3
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0, 1, 2, 3, -1, -2, 4, 5, 6, -3, -4, 7, 8, 9, -5, -6, 10, 11, 12, -7, -8, 13, 14, 15, -9, -10, 16, 17, 18, -11, -12, 19, 20, 21, -13, -14, 22, 23, 24, -15, -16, 25, 26, 27, -17, -18, 28, 29, 30, -19, -20, 31, 32, 33, -21, -22, 34, 35, 36, -23, -24, 37, 38, 39, -25, -26, 40, 41
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OFFSET
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0,3
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COMMENTS
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This sequence enumerates the denominators with sign in case p=3 and n=2 of:
log(p/n) = sum( i>=0, sum(p*i+1<=j<=p*(i+1),1/j) - sum(n*i+1<=j<=n*(i+1),1/j) )
Similar sequences can be constructed for the logarithm of any rational r=p/n (p,n>0), enumerating p positive integers and n negative integers every p+n terms.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1)
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FORMULA
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Sum_{k>0} 1/a(k) = log(3/2).
G.f.: x*(1+2*x+3*x^2-x^3-2*x^4+2*x^5+x^6-x^8)/((x-1)^2*(x^4+x^3+x^2+x+1)^2 ).
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 2, 0, 0, 0, 0, -1}, {0, 1, 2, 3, -1, -2, 4, 5, 6, -3}, 100] (* G. C. Greubel, May 27 2016 *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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