OFFSET
0,3
COMMENTS
A twice-partition of n (A063834) is a sequence of integer partitions, one of each part of an integer partition of n.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5000
EXAMPLE
The a(1) = 1 through a(6) = 18 twice-partitions counted by this sequence:
(1) (2) (3) (4) (5) (6)
(11) (111) (22) (3)(2) (33)
(2)(1) (1111) (4)(1) (222)
(11)(1) (3)(1) (11111) (4)(2)
(11)(2) (22)(1) (5)(1)
(2)(11) (3)(11) (22)(2)
(111)(1) (111)(2) (4)(11)
(111)(11) (111111)
(1111)(1) (111)(3)
(11)(2)(1) (22)(11)
(2)(11)(1) (3)(111)
(1111)(2)
(3)(2)(1)
(1111)(11)
(11111)(1)
(3)(11)(1)
(111)(2)(1)
(111)(11)(1)
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(j!*
binomial(numtheory[tau](i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..45); # Alois P. Heinz, Sep 08 2025
MATHEMATICA
twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn], {ptn, IntegerPartitions[n]}];
Table[Length[Select[twiptn[n], UnsameQ@@#&&And@@SameQ@@@#&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 07 2025
EXTENSIONS
More terms from Alois P. Heinz, Sep 08 2025
STATUS
approved