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1, 1, 1, -1, 0, 1, 1, 1, 0, 1, -1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Row sums = A104117: (1, 2, 0, 3, 0, 0, 0, 4, 0, 0, ...).
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LINKS
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FORMULA
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
-1, 0, 1;
1, 1, 0, 1;
-1, 0, 0, 0, 1;
-1, -1, 1, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 1;
1, 1, 0, 1, 0, 0, 0, 1;
...
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MATHEMATICA
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T[n_, k_] := If[Divisible[n, k], MoebiusMu[(n/k)/2^IntegerExponent[n/k, 2]], 0];
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PROG
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(PARI) tabl(nn) = {Tm = matrix(nn, nn, n, k, if (! (n % k), moebius(n/k), 0)); Tr = matrix(nn, nn, n, k, n--; k--; if ((n==k), 1, if (n==2*k+1, -1, 0))); Ti = Tr^(-1); Tp = Tm*Ti*Ti; for (n=1, nn, for (k=1, n, print1(Tp[n, k], ", "); ); print(); ); }
(PARI) T(n, k)={ if(n%k, 0, sumdiv(n/k, d, my(e=valuation(d, 2)); if(d==1<<e, moebius(n/(k*d))*(1 + e), 0))) } \\ Andrew Howroyd, Aug 03 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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