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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).
2
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.
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}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved