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A242089
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Number of triples (a,b,c) with 0 < a < b < c < p and a + b + c == 0 mod p, where p = prime(n).
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2
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0, 0, 0, 2, 10, 16, 32, 42, 66, 112, 130, 192, 240, 266, 322, 416, 522, 560, 682, 770, 816, 962, 1066, 1232, 1472, 1600, 1666, 1802, 1872, 2016, 2562, 2730, 2992, 3082, 3552, 3650, 3952, 4266, 4482, 4816, 5162, 5280, 5890, 6016, 6272, 6402, 7210, 8066, 8362, 8512
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OFFSET
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1,4
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COMMENTS
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a(n) is even. (Proof. Each triple (a,b,c) with b < p/2 pairs uniquely with a triple (a',b',c') = (p-c,p-b,p-a) with b' > p/2.)
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LINKS
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FORMULA
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EXAMPLE
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For prime(4) = 7 there are 2 triples (a,b,c) with 0 < a < b < c < 7 and a + b + c == 0 mod 7, namely, 1+2+4 = 7 and 3+5+6 = 2*7, so a(4) = 2.
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MATHEMATICA
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Table[ Length[ Reduce[ Mod[a + b + c, Prime[n]] == 0 && 0 < a < b < c < Prime[n], {a, b, c}, Integers]], {n, 40}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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