Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Sep 13 2020 14:45:36
%S 0,0,0,0,1,0,1,2,2,3,5,5,9,10,15,18,24,30,40,47,65,76,97,120,150,179,
%T 229,270,336,404,494,588,722,852,1035,1227,1476,1744,2090,2461,2935,
%U 3446,4092,4795,5665,6627,7801,9096,10680,12426,14528,16881,19680,22800,26525
%N Number of partitions of n with equal nonzero number of parts congruent to each of 0 and 1 (mod 3).
%p b := proc(n, i, t, s) option remember; `if`(n=0,
%p `if`(t = s and t >= 1, 1, 0), `if`(i<1, 0, b(n, i-1, t, s)+
%p b(n-i, min(n-i, i), t + [1, 0, 0][1+irem(i, 3)], s + [0, 1, 0][1+irem(i, 3)])))
%p end:
%p seq(b(n,n, 0,0), n=0..50); # _Georg Fischer_, Sep 13 2020
%t equalQ[partit_] := With[{t = Total[Switch[Mod[#, 3], 0, {1, 0, 0}, 1, {0, 1, 0}, 2, {0, 0, 1}]& /@ partit]}, t[[1]] > 0 && t[[1]] == t[[2]]]; a[n_] := Select[IntegerPartitions[n], equalQ] // Length; a[0] = 0; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 54}] (* _Jean-François Alcover_, Dec 07 2016 *)
%K nonn
%O 0,8
%A _Olivier Gérard_