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%I #8 Aug 16 2024 15:08:23
%S 1,1,1,2,2,4,4,6,8,11,12,18,21,28,33,43,52,66,78,98,116,145,171,209,
%T 247,300,352,424,499,595,695,826,963,1138,1322,1553,1802,2106,2435,
%U 2835,3271,3795,4365,5046,5792,6673,7641,8778,10030,11490,13099,14968,17030
%N Number of integer partitions of n whose maximal anti-runs have distinct minima.
%C These are partitions with no part appearing more than twice and with the least part appearing only once.
%C Also the number of reversed integer partitions of n whose maximal anti-runs have distinct minima.
%e 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).
%e The a(1) = 1 through a(9) = 11 partitions:
%e (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e (12) (13) (14) (15) (16) (17) (18)
%e (23) (24) (25) (26) (27)
%e (122) (123) (34) (35) (36)
%e (124) (125) (45)
%e (133) (134) (126)
%e (233) (135)
%e (1223) (144)
%e (234)
%e (1224)
%e (1233)
%t Table[Length[Select[IntegerPartitions[n], UnsameQ@@Min/@Split[#,UnsameQ]&]],{n,0,30}]
%Y Includes all strict partitions A000009.
%Y For identical instead of distinct leaders we have A115029.
%Y A version for compositions instead of partitions is A374518, ranks A374638.
%Y For minima instead of maxima we have A375133, ranks A375402.
%Y These partitions have ranks A375398.
%Y The complement is counted by A375404, ranks A375399.
%Y A000041 counts integer partitions.
%Y A003242 counts anti-run compositions, ranks A333489.
%Y A011782 counts integer compositions.
%Y A055887 counts sequences of partitions with total sum n.
%Y A375128 lists minima of maximal anti-runs of prime indices, sums A374706.
%Y Cf. A034296, A141199, A358830, A358836, A358905, A374704, A374757, A374758, A374761, A375136, A375400, A375401.
%K nonn,new
%O 0,4
%A _Gus Wiseman_, Aug 14 2024
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