

A301766


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


3



1, 1, 1, 3, 4, 6, 7, 9, 11, 13, 16, 19, 22, 26, 32, 36, 42, 52, 59, 66, 79, 93, 108, 125, 141, 162, 192, 222, 248, 285, 331, 375, 430, 492, 555, 632, 719, 816, 929, 1051, 1177, 1327, 1510, 1701, 1908, 2146, 2408, 2705, 3035, 3388, 3792, 4257, 4751, 5284, 5894
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OFFSET

1,4


COMMENTS

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


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000


EXAMPLE

The a(9) = 11 rooted twicepartitions:
(7), (1111111),
(6)(), (33)(), (222)(), (111111)(), (11111)(1), (22)(2), (1111)(11),
(1111)(1)(), (111)(11)().


MATHEMATICA

twirtns[n_]:=Join@@Table[Tuples[IntegerPartitions[#1]&/@ptn], {ptn, IntegerPartitions[n1]}];
Table[Select[twirtns[n], UnsameQ@@Total/@#&&SameQ@@Join@@#&]//Length, {n, 20}]


PROG

(PARI) a(n)=if(n<3, 1, sum(k=1, n2, polcoef(prod(j=0, (n2)\k, 1 + x^(j*k + 1) + O(x^n)), n1))) \\ Andrew Howroyd, Aug 26 2018


CROSSREFS

Cf. A002865, A032305, A047966, A063834, A093637, A296134, A300383, A301422, A301462, A301467, A301480, A301706.
Sequence in context: A286809 A244239 A006855 * A229173 A066499 A201471
Adjacent sequences: A301763 A301764 A301765 * A301767 A301768 A301769


KEYWORD

nonn


AUTHOR

Gus Wiseman, Mar 26 2018


EXTENSIONS

Terms a(26) and beyond from Andrew Howroyd, Aug 26 2018


STATUS

approved



