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

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

Cf. A002865, A032305, A063834, A093637, A127524, A279791, A296133, A301422, A301462, A301467, A301480, A301706.

Sequence in context: A173513 A367693 A147663 * A374210 A036811 A330265

Adjacent sequences: A301762 A301763 A301764 * A301766 A301767 A301768

Keyword

nonn,more

Author

Gus Wiseman, Mar 26 2018

Status

approved