A301765 - OEIS

A301765

Number of rooted twice-partitions of n where the first rooted partition is constant and the composite rooted partition is strict, i.e., of type (Q,R,Q).

1, 1, 2, 2, 3, 3, 4, 5, 8, 7, 11, 11, 19, 16, 27, 23, 42, 33, 63, 47, 87, 71, 119, 90, 195

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

A rooted partition of n is an integer partition of n - 1. A rooted twice-partition of n is a choice of a rooted partition of each part in a rooted partition of n.

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

The a(9) = 8 rooted twice-partitions:

(7), (61), (52), (43), (421),

(3)(21), (21)(3),

()()()()()()()().

MATHEMATICA

twirtns[n_]:=Join@@Table[Tuples[IntegerPartitions[#-1]&/@ptn], {ptn, IntegerPartitions[n-1]}];

Table[Select[twirtns[n], SameQ@@Total/@#&&UnsameQ@@Join@@#&]//Length, {n, 20}]

CROSSREFS