OFFSET
0,2
COMMENTS
a(0) = 1 corresponds to the empty sum, in which all terms are colored in one among three given colors, since there is no term at all.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..50
FORMULA
a(n) = Sum_{k=1..n} A091298(n,k)*3^k.
EXAMPLE
For n = 1, there is only the partition [1], which can be colored in any of the three colors, whence a(1) = 3.
For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 3 + 9 + 9 = 21 distinct possibilities.
PROG
(PARI) a(n)=sum(k=1, n, A091298(n, k)*3^k, !n)
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Sep 22 2018
EXTENSIONS
a(12) corrected and a(13)-a(24) added by Alois P. Heinz, Sep 24 2018
STATUS
approved