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A358826
Number of ways to choose a sequence of partitions, one of each part of an odd-length partition of 2n+1 into odd parts.
3
1, 4, 11, 35, 113, 326, 985, 3124, 8523, 24519, 71096, 191940, 530167, 1442059, 3833007, 10243259, 27151086, 71032191, 184492464, 478339983, 1227208513, 3140958369, 8016016201, 20210235189, 50962894061, 127936646350, 319022819270, 794501931062, 1969154638217
OFFSET
0,2
EXAMPLE
The a(1) = 1 through a(5) = 11 twice-partitions:
(1) (3) (5)
(21) (32)
(111) (41)
(1)(1)(1) (221)
(311)
(2111)
(11111)
(3)(1)(1)
(21)(1)(1)
(111)(1)(1)
(1)(1)(1)(1)(1)
MATHEMATICA
twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn], {ptn, IntegerPartitions[n]}];
Table[Length[Select[twiptn[n], OddQ[Length[#]]&&OddQ[Times@@Total/@#]&]], {n, 1, 15, 2}]
CROSSREFS
For odd parts instead of length and sums we have A270995.
Requiring odd lengths and odd parts gives A279374 aerated.
This is the case of A358824 with odd sums.
This is the odd-length case (hence odd bisection) of A358825.
For odd lengths (instead of length) we have A358827.
For odd lengths instead of sums we have A358834.
A000009 counts partitions into odd parts.
A027193 counts partitions of odd length.
A063834 counts twice-partitions, strict A296122, row-sums of A321449.
A078408 counts odd-length partitions into odd parts.
A300301 aerated counts twice-partitions with odd sums and parts.
Sequence in context: A052550 A197626 A349185 * A212910 A339034 A114248
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 03 2022
STATUS
approved