[seqfan] Re: 0,1,3,6,15,33,66,155,333,666

[Richard J. Mathar]

On behalf of http://list.seqfan.eu/pipermail/seqfan/2017-June/017696.html :
This has recurrence
  a(n)= +11*a(n-3) -10*a(n-6)
and generating function 
  G.f.: (1+x)*(4*x^2+2*x+1) / ( (x-1)*(1+x+x^2)*(10*x^3-1) ).
It is constructed by starting with 0, 1, 3 and attaching a 6 to the decimal
representation of a(n-3) if n == 0 (mod 3), attaching a 5 to the decimal
representation of a(n-3) if n == 1 (mod 3), and attaching a 3 to the
decimal representation of a(n-3) if n == 2 (mod 3).
Trisections: A099915, A002280, A002277.