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A375134
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Number of integer partitions of n whose maximal anti-runs have distinct minima.
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1
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1, 1, 1, 2, 2, 4, 4, 6, 8, 11, 12, 18, 21, 28, 33, 43, 52, 66, 78, 98, 116, 145, 171, 209, 247, 300, 352, 424, 499, 595, 695, 826, 963, 1138, 1322, 1553, 1802, 2106, 2435, 2835, 3271, 3795, 4365, 5046, 5792, 6673, 7641, 8778, 10030, 11490, 13099, 14968, 17030
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OFFSET
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0,4
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COMMENTS
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These are partitions with no part appearing more than twice and with the least part appearing only once.
Also the number of reversed integer partitions of n whose maximal anti-runs have distinct minima.
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LINKS
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EXAMPLE
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The partition y = (6,5,5,4,3,3,2,1) has maximal anti-runs ((6,5),(5,4,3),(3,2,1)), with minima (5,3,1), so y is counted under a(29).
The a(1) = 1 through a(9) = 11 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(12) (13) (14) (15) (16) (17) (18)
(23) (24) (25) (26) (27)
(122) (123) (34) (35) (36)
(124) (125) (45)
(133) (134) (126)
(233) (135)
(1223) (144)
(234)
(1224)
(1233)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@Min/@Split[#, UnsameQ]&]], {n, 0, 30}]
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CROSSREFS
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Includes all strict partitions A000009.
For identical instead of distinct leaders we have A115029.
A version for compositions instead of partitions is A374518, ranks A374638.
These partitions have ranks A375398.
A011782 counts integer compositions.
A055887 counts sequences of partitions with total sum n.
A375128 lists minima of maximal anti-runs of prime indices, sums A374706.
Cf. A034296, A141199, A358830, A358836, A358905, A374704, A374757, A374758, A374761, A375136, A375400, A375401.
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KEYWORD
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nonn,new
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AUTHOR
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STATUS
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approved
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