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A046765
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Number of partitions of n with equal number of parts congruent to each of 0, 1 and 2 (mod 3).
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14
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1, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 7, 0, 0, 13, 0, 0, 25, 0, 0, 43, 0, 0, 77, 0, 0, 130, 0, 0, 222, 0, 0, 365, 0, 0, 603, 0, 0, 966, 0, 0, 1546, 0, 0, 2425, 0, 0, 3783, 0, 0, 5813, 0, 0, 8884, 0, 0, 13411, 0, 0, 20130, 0, 0, 29922, 0, 0, 44217, 0, 0, 64814, 0, 0, 94485, 0, 0
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OFFSET
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0,10
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} x^(6*k)/(Product_{j=1..k} 1 - x^(3*j))^3. - Andrew Howroyd, Sep 16 2019
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MATHEMATICA
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Table[Length[Select[Last /@ Transpose /@ Tally /@ Mod[IntegerPartitions[n], 3], Length[#] == 3 && Length[Union[#]] == 1 &]], {n, 50}] (* Jayanta Basu, Jun 28 2013 *)
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PROG
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(PARI) seq(n)={Vec(sum(k=0, n\6, x^(6*k)/prod(j=1, k, 1 - x^(3*j) + O(x*x^n))^3) + O(x*x^n))} \\ Andrew Howroyd, Sep 16 2019
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CROSSREFS
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Other similar sequences include:
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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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