cp's OEIS Frontend

A381544 Number of integer partitions of n not containing more ones than any other part.

%I A381544 #6 Mar 25 2025 08:57:42
%S A381544 0,0,1,2,3,4,7,8,13,17,24,30,45,54,75,97,127,160,212,263,342,427,541,
%T A381544 672,851,1046,1307,1607,1989,2428,2993,3631,4443,5378,6533,7873,9527,
%U A381544 11424,13752,16447,19701,23470,28016,33253,39537,46801,55428,65408,77238
%N A381544 Number of integer partitions of n not containing more ones than any other part.
%e A381544 The a(2) = 1 through a(9) = 17 partitions:
%e A381544   (2)  (3)   (4)   (5)    (6)     (7)     (8)      (9)
%e A381544        (21)  (22)  (32)   (33)    (43)    (44)     (54)
%e A381544              (31)  (41)   (42)    (52)    (53)     (63)
%e A381544                    (221)  (51)    (61)    (62)     (72)
%e A381544                           (222)   (322)   (71)     (81)
%e A381544                           (321)   (331)   (332)    (333)
%e A381544                           (2211)  (421)   (422)    (432)
%e A381544                                   (2221)  (431)    (441)
%e A381544                                           (521)    (522)
%e A381544                                           (2222)   (531)
%e A381544                                           (3221)   (621)
%e A381544                                           (3311)   (3222)
%e A381544                                           (22211)  (3321)
%e A381544                                                    (4221)
%e A381544                                                    (22221)
%e A381544                                                    (32211)
%e A381544                                                    (222111)
%t A381544 Table[Length[Select[IntegerPartitions[n],Count[#,1]<=Max@@Length/@Split[DeleteCases[#,1]]&]],{n,0,30}]
%Y A381544 The complement is counted by A241131, ranks A360013 = 2*A360015 (if we prepend 1).
%Y A381544 The Heinz numbers of these partitions are A381439.
%Y A381544 The case of equality is A382303, ranks A360014.
%Y A381544 A000041 counts integer partitions, strict A000009.
%Y A381544 A008284 counts partitions by length, strict A008289.
%Y A381544 A047993 counts partitions with max part = length, ranks A106529.
%Y A381544 A091602 counts partitions by the greatest multiplicity, rank statistic A051903.
%Y A381544 A116598 counts ones in partitions, rank statistic A007814.
%Y A381544 A239964 counts partitions with max multiplicity = length, ranks A212166.
%Y A381544 A240312 counts partitions with max part = max multiplicity, ranks A381542.
%Y A381544 A382302 counts partitions with max = max multiplicity = distinct length, ranks A381543.
%Y A381544 Cf. A047966, A091605, A116861, A232697, A237984, A362608, A363724, A381079, A381437, A381438.
%K A381544 nonn
%O A381544 0,4
%A A381544 _Gus Wiseman_, Mar 24 2025