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A360079
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Finite differences of Moebius function for the floor quotient poset.
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2
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1, -2, 0, 1, 0, 1, 0, -1, 1, 0, 0, -1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2
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OFFSET
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1,2
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COMMENTS
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a(n) = mu(n) - mu(n-1), where mu(n) = A360078(n) is the Moebius function of the floor quotient poset.
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LINKS
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MATHEMATICA
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LinearSolve[Table[If[Floor[i/j] > Floor[i/(j + 1)], 1, 0], {i, n}, {j, n}] . Table[If[i >= j, 1, 0], {i, n}, {j, n}], UnitVector[n, 1]]
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PROG
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(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, my(S=Set(vector(n-1, k, n\(k+1)))); v[n]=-sum(i=1, #S, v[S[i]])); vector(#v, i, v[i]-if(i>1, v[i-1]))} \\ Andrew Howroyd, Jan 24 2023
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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