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%I #14 Sep 16 2019 16:23:15
%S 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,
%T 222,0,0,365,0,0,603,0,0,966,0,0,1546,0,0,2425,0,0,3783,0,0,5813,0,0,
%U 8884,0,0,13411,0,0,20130,0,0,29922,0,0,44217,0,0,64814,0,0,94485,0,0
%N Number of partitions of n with equal number of parts congruent to each of 0, 1 and 2 (mod 3).
%H Andrew Howroyd, <a href="/A046765/b046765.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Sum_{k>=0} x^(6*k)/(Product_{j=1..k} 1 - x^(3*j))^3. - _Andrew Howroyd_, Sep 16 2019
%t Table[Length[Select[Last /@ Transpose /@ Tally /@ Mod[IntegerPartitions[n], 3], Length[#] == 3 && Length[Union[#]] == 1 &]], {n, 50}] (* _Jayanta Basu_, Jun 28 2013 *)
%o (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
%Y Other similar sequences include:
%Y Mod 4: A046766, A046767, A046768, A046769, A046770.
%Y Mod 5: A046771, A046772, A046773, A046774, A046775, A046776.
%K nonn
%O 0,10
%A _David W. Wilson_
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