%I
%S 0,1,2,5,9,14,21,30,41,54,70,89,110,135,164,195,231,272,315,364,419,
%T 476,540,611,684,765,854,945,1045,1154,1265,1386,1517,1650,1794,1949,
%U 2106,2275,2456,2639,2835,3044,3255,3480,3719,3960,4216,4487,4760,5049,5354
%N Number of edges in the graded poset of the partitions of n taken modulo 3, where a partition into k parts is joined to a partition into k+1 parts if the latter is a refinement of the former.
%H Alois P. Heinz, <a href="/A276031/b276031.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: (x^62*x^5+x^4x^3+2*x^2+1)*x^2/((x^2+x+1)^2*(x1)^4).  _Alois P. Heinz_, Aug 27 2016
%e a(6) = 14, the 14 edges are: (111111)  (21111), (21111)  (1110), (21111)  (2211), (1110)  (111), (1110)  (210), (2211)  (111), (2211)  (210), (2211)  (222), (210)  (00), (210)  (21), (111)  (21), (222)  (21), (00)  (0), (21)  (0).
%Y Cf. A000097, A140144.
%K nonn
%O 1,3
%A _Caleb Ji_, Aug 17 2016
%E More terms from _Alois P. Heinz_, Aug 27 2016
