[seqfan] A class of partitions.

[L. Edson Jeffery]

Related to certain rhombus substitution tilings (the Penrose tilings in
particular):

For n = 1,2,..., what is the number of partitions of 2*n+1 with at least
three parts and no part greater than n? I counted these partitions by hand
for the first few n, so I know that the sequence starts {1, 3, 8, 18, 37,
70, ...}, unless I made a mistake.

I could not find this sequence in OEIS, possibly because it might be a
bisection of another sequence already there (and which I also cannot find).
Would someone please calculate enough terms and consider adding the
sequence to the database and let me know the A-number so I can find it?

Ed Jeffery