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A301750 Number of rooted twice-partitions of n where the composite rooted partition is strict. 3
1, 1, 2, 3, 5, 8, 12, 18, 29, 42, 61, 86, 127, 181, 257, 352, 489, 668, 935, 1270, 1730, 2312, 3101, 4112, 5533, 7345, 9742, 12785, 16793, 21821, 28452, 36908, 48108, 62198, 80337, 103081, 132372, 168805, 215247, 273678 (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..40.

EXAMPLE

The a(8) = 18 rooted twice-partitions where the composite rooted partition is strict:

(6), (51), (42), (321),

(5)(), (41)(), (32)(), (4)(1), (3)(2),

(4)()(), (31)()(), (3)(1)(),

(3)()()(), (21)()()(), (2)(1)()(),

(2)()()()(),

(1)()()()()(),

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

MATHEMATICA

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

Table[Select[twirtns[n], UnsameQ@@Join@@#&]//Length, {n, 30}]

CROSSREFS

Cf. A002865, A063834, A093637, A127524, A279790, A294788, A301422, A301462, A301467, A301480, A301706.

Sequence in context: A130732 A018135 A065435 * A086676 A055804 A267372

Adjacent sequences:  A301747 A301748 A301749 * A301751 A301752 A301753

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 26 2018

STATUS

approved

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Last modified August 18 09:01 EDT 2022. Contains 356204 sequences. (Running on oeis4.)