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A178086
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Triangle T(n,m) = - phi(n+1) + phi(m+1) + phi(n-m+1), 0<=m<=n, where phi = A000010 is Euler's totient.
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1
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1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, -1, 0, -1, 1, 1, 3, 2, 2, 3, 1, 1, -3, 0, -2, 0, -3, 1, 1, 3, 0, 2, 2, 0, 3, 1, 1, -1, 2, -2, 2, -2, 2, -1, 1, 1, 3, 2, 4, 2, 2, 4, 2, 3, 1, 1, -5, -2, -4, 0, -6, 0, -4, -2, -5, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,17
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COMMENTS
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Row sums are 1, 2, 2, 4, 0, 12, -6, 12, 2, 24, -26,...
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LINKS
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FORMULA
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T(n,m) = T(n,n-m).
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EXAMPLE
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1;
1, 1;
1, 0, 1;
1, 1, 1, 1;
1, -1, 0, -1, 1;
1, 3, 2, 2, 3, 1;
1, -3, 0, -2, 0, -3, 1;
1, 3, 0, 2, 2, 0, 3, 1;
1, -1, 2, -2, 2, -2, 2, -1, 1;
1, 3, 2, 4, 2, 2, 4, 2, 3, 1;
1, -5, -2, -4, 0, -6, 0, -4, -2, -5, 1;
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MAPLE
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-numtheory[phi](n+1)+numtheory[phi](m+1)+numtheory[phi](n-m+1)
end proc;
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MATHEMATICA
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T[n_, m_, q_] := 1 - EulerPhi[n + q] + (EulerPhi[m + q] + EulerPhi[n - m + q]) - EulerPhi[q];
Table[Flatten[Table[Table[T[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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