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A244504
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Number of distinct lines passing through at least two points in a triangular grid of side n.
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2
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3, 9, 24, 51, 102, 177, 294, 459, 690, 987, 1380, 1875, 2508, 3279, 4212, 5319, 6648, 8199, 10026, 12141, 14580, 17343, 20496, 24051, 28068, 32547, 37542, 43071, 49218, 55983, 63456, 71661, 80658, 90447, 101100, 112635, 125160, 138675, 153252, 168915, 185784
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OFFSET
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2,1
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LINKS
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FORMULA
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a(n) = 3*sum(j = 1..n-1, euler_phi(j)*(g(n-j)-g(n-2*j))), where g(i) = i*(i+1)/2 if i > 0, otherwise 0, after Jon E. Schoenfield.
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MATHEMATICA
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PROG
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(PARI) g(j) = if (j > 0, j*(j+1)/2, 0);
a(n) = 3*sum(j = 1, n-1, eulerphi(j)*(g(n-j)-g(n-2*j))); \\ Michel Marcus, Sep 04 2014
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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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