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A320226
Number of integer partitions of n whose non-1 parts are all equal.
5
1, 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 19, 24, 25, 28, 31, 35, 36, 41, 42, 47, 50, 53, 54, 61, 63, 66, 69, 74, 75, 82, 83, 88, 91, 94, 97, 105, 106, 109, 112, 119, 120, 127, 128, 133, 138, 141, 142, 151, 153, 158, 161, 166, 167, 174, 177, 184, 187, 190, 191, 202
OFFSET
0,3
LINKS
Jonathan Bloom, Nathan McNew, Counting pattern-avoiding integer partitions, arXiv:1908.03953 [math.CO], 2019.
FORMULA
a(n > 1) = A002541(n - 1) + 1.
EXAMPLE
The integer partitions whose non-1 parts are all equal:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (21) (22) (41) (33) (61) (44)
(111) (31) (221) (51) (331) (71)
(211) (311) (222) (511) (611)
(1111) (2111) (411) (2221) (2222)
(11111) (2211) (4111) (3311)
(3111) (22111) (5111)
(21111) (31111) (22211)
(111111) (211111) (41111)
(1111111) (221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], SameQ@@DeleteCases[#, 1]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 07 2018
STATUS
approved