OFFSET
0,6
COMMENTS
The version for all k = 0..n is A113685 (including zeros).
EXAMPLE
Triangle begins:
1
1
1 1
1 2
2 1 2
2 2 3
3 2 2 4
3 4 3 5
5 3 4 4 6
5 6 6 5 8
7 5 6 8 6 10
7 10 9 10 8 12
11 7 10 12 12 10 15
11 14 15 15 16 12 18
15 11 14 20 18 20 15 22
15 22 21 25 24 24 18 27
Row n = 8 counts the following partitions:
(8) (611) (431) (521) (71)
(62) (4211) (41111) (332) (53)
(44) (22211) (3221) (32111) (5111)
(422) (221111) (2111111) (3311)
(2222) (311111)
(11111111)
Row n = 9 counts the following partitions:
(81) (63) (54) (72) (9)
(621) (6111) (522) (5211) (711)
(441) (432) (4311) (3321) (531)
(4221) (42111) (411111) (321111) (51111)
(22221) (3222) (32211) (21111111) (333)
(222111) (2211111) (33111)
(3111111)
(111111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Total[Select[#, OddQ]]==k&]], {n, 0, 15}, {k, Mod[n, 2], n, 2}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Oct 16 2023
STATUS
approved