This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108711 #11 Nov 27 2019 01:29:52
%S A108711 0,1,1,2,2,2,3,3,3,5,5,5,7,7,7,11,11,11,15,15,15,22,22,22,30,30,30,42,
%T A108711 42,42,56,56,56,77,77,77,101,101,101,135,135,135,176,176,176,231,231,
%U A108711 231,297,297,297,385,385,385,490,490,490,627,627,627,792,792,792,1002
%N A108711 Number of partitions of n with floor(2n/3) parts.
%C A108711 It would be interesting to know whether the sequence continues with runs of length 3 of terms of equal values.
%C A108711 The number of partitions of n with floor(2n/3) = A004523(n) parts equals the number of partitions of n with maximum part floor(2n/3). This leaves n-floor(2n/3) = ceiling(n/3) = A002264(n+2) as the sum of all the other parts, with no further restriction since floor(2n/3) >= ceiling(n/3) remains the largest part for any partition of the remainder, at least for n > 1. Since A002264 triplicates the integers, this sequence here triplicates the entries of A000041. - _R. J. Mathar_, Jul 31 2010, Feb 22 2012
%e A108711 The partitions of 6 are {{6},{5,1},{4,2},{4,1,1},{3,3},{3,2,1},{3,1,1,1},{2,2,2},{2,2,1,1},{2,1,1,1,1},{1,1,1,1,1,1}}, of which 2 have 4 parts. Thus a(6)=2.
%Y A108711 Cf. A066639.
%K A108711 nonn
%O A108711 1,4
%A A108711 _John W. Layman_, Jun 20 2005
%E A108711 Sequence extended by _R. J. Mathar_, Jul 31 2010