cp's OEIS Frontend

A363947 Number of integer partitions of n with mean < 3/2.

%I A363947 #14 Jul 09 2023 08:33:40
%S A363947 0,1,1,1,2,2,2,4,4,4,7,7,7,12,12,12,19,19,19,30,30,30,45,45,45,67,67,
%T A363947 67,97,97,97,139,139,139,195,195,195,272,272,272,373,373,373,508,508,
%U A363947 508,684,684,684,915,915,915,1212,1212,1212,1597,1597,1597,2087
%N A363947 Number of integer partitions of n with mean < 3/2.
%e A363947 The partition y = (2,2,1) has mean 5/3, which is not less than 3/2, so y is not counted under 5.
%e A363947 The a(1) = 1 through a(8) = 4 partitions:
%e A363947   (1)  (11)  (111)  (211)   (2111)   (21111)   (22111)    (221111)
%e A363947                     (1111)  (11111)  (111111)  (31111)    (311111)
%e A363947                                                (211111)   (2111111)
%e A363947                                                (1111111)  (11111111)
%t A363947 Table[Length[Select[IntegerPartitions[n],Round[Mean[#]]==1&]],{n,0,15}]
%Y A363947 The high version is A000012 (all ones).
%Y A363947 This is A000070 with each term repeated three times (see A025065 for two).
%Y A363947 These partitions have ranks A363948.
%Y A363947 The complement is counted by A364059.
%Y A363947 A008284 counts partitions by length, A058398 by mean.
%Y A363947 A051293 counts subsets with integer mean, median A000975.
%Y A363947 A067538 counts partitions with integer mean, strict A102627, ranks A316413.
%Y A363947 A327482 counts partitions by integer mean.
%Y A363947 A349156 counts partitions with non-integer mean, ranks A348551.
%Y A363947 Cf. A000041, A002865, A026905, A027336, A237984, A241131, A327472, A363724, A363745, A363943, A363949.
%K A363947 nonn
%O A363947 0,5
%A A363947 _Gus Wiseman_, Jul 02 2023