cp's OEIS Frontend

A333190 Number of integer partitions of n whose run-lengths are either strictly increasing or strictly decreasing.

%I A333190 #9 May 18 2020 06:38:01
%S A333190 1,1,2,2,4,5,7,10,13,15,21,26,29,39,49,50,68,80,92,109,129,142,181,
%T A333190 201,227,262,317,343,404,456,516,589,677,742,870,949,1077,1207,1385,
%U A333190 1510,1704,1895,2123,2352,2649,2877,3261,3571,3966,4363,4873,5300,5914,6466
%N A333190 Number of integer partitions of n whose run-lengths are either strictly increasing or strictly decreasing.
%e A333190 The a(1) = 1 through a(8) = 13 partitions:
%e A333190   (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
%e A333190        (11)  (111)  (22)    (221)    (33)      (322)      (44)
%e A333190                     (211)   (311)    (222)     (331)      (332)
%e A333190                     (1111)  (2111)   (411)     (511)      (422)
%e A333190                             (11111)  (3111)    (2221)     (611)
%e A333190                                      (21111)   (4111)     (2222)
%e A333190                                      (111111)  (22111)    (5111)
%e A333190                                                (31111)    (22211)
%e A333190                                                (211111)   (41111)
%e A333190                                                (1111111)  (221111)
%e A333190                                                           (311111)
%e A333190                                                           (2111111)
%e A333190                                                           (11111111)
%t A333190 Table[Length[Select[IntegerPartitions[n],Or[Less@@Length/@Split[#],Greater@@Length/@Split[#]]&]],{n,0,30}]
%Y A333190 The non-strict version is A332745.
%Y A333190 The generalization to compositions is A333191.
%Y A333190 Partitions with distinct run-lengths are A098859.
%Y A333190 Partitions with strictly increasing run-lengths are A100471.
%Y A333190 Partitions with strictly decreasing run-lengths are A100881.
%Y A333190 Partitions with weakly decreasing run-lengths are A100882.
%Y A333190 Partitions with weakly increasing run-lengths are A100883.
%Y A333190 Partitions with unimodal run-lengths are A332280.
%Y A333190 Partitions whose run-lengths are not increasing nor decreasing are A332641.
%Y A333190 Compositions whose run-lengths are unimodal or co-unimodal are A332746.
%Y A333190 Compositions that are neither increasing nor decreasing are A332834.
%Y A333190 Strictly increasing or strictly decreasing compositions are A333147.
%Y A333190 Compositions with strictly increasing run-lengths are A333192.
%Y A333190 Numbers with strictly increasing prime multiplicities are A334965.
%Y A333190 Cf. A032020, A059204, A072706, A332726, A332831, A332833, A332835, A333149.
%K A333190 nonn
%O A333190 0,3
%A A333190 _Gus Wiseman_, May 17 2020