cp's OEIS Frontend

A375404 Number of integer partitions of n whose minima of maximal anti-runs are not all different.

%I A375404 #6 Aug 17 2024 21:50:33
%S A375404 0,0,1,1,3,3,7,9,14,19,30,38,56,73,102,133,179,231,307,392,511,647,
%T A375404 831,1046,1328,1658,2084,2586,3219,3970,4909,6016,7386,9005,10988,
%U A375404 13330,16175,19531,23580,28350,34067,40788,48809,58215,69383,82461,97917,115976
%N A375404 Number of integer partitions of n whose minima of maximal anti-runs are not all different.
%C A375404 An anti-run is a sequence with no adjacent equal terms. The minima of maximal anti-runs in a sequence are obtained by splitting it into maximal anti-run subsequences and taking the least term of each.
%C A375404 Also the number of reversed integer partitions of n such that the minima of maximal anti-runs are not all different.
%e A375404 The a(0) = 0 through a(8) = 14 reversed partitions:
%e A375404   .  .  (11)  (111)  (22)    (113)    (33)      (115)      (44)
%e A375404                      (112)   (1112)   (114)     (223)      (116)
%e A375404                      (1111)  (11111)  (222)     (1114)     (224)
%e A375404                                       (1113)    (1123)     (1115)
%e A375404                                       (1122)    (1222)     (1124)
%e A375404                                       (11112)   (11113)    (1133)
%e A375404                                       (111111)  (11122)    (2222)
%e A375404                                                 (111112)   (11114)
%e A375404                                                 (1111111)  (11123)
%e A375404                                                            (11222)
%e A375404                                                            (111113)
%e A375404                                                            (111122)
%e A375404                                                            (1111112)
%e A375404                                                            (11111111)
%t A375404 Table[Length[Select[IntegerPartitions[n], !UnsameQ@@Min/@Split[#,UnsameQ]&]],{n,0,30}]
%Y A375404 The complement for maxima instead of minima is A375133, ranks A375402.
%Y A375404 The complement is counted by A375134, ranks A375398.
%Y A375404 These partitions are ranked by A375399.
%Y A375404 For maxima instead of minima we have A375401, ranks A375403.
%Y A375404 For identical instead of distinct we have A375405, ranks A375397.
%Y A375404 A000041 counts integer partitions, strict A000009.
%Y A375404 A003242 counts anti-run compositions, ranks A333489.
%Y A375404 A055887 counts sequences of partitions with total sum n.
%Y A375404 A375128 lists minima of maximal anti-runs of prime indices, sums A374706.
%Y A375404 Cf. A034296, A046660, A073492, A115029, A141199, A239955, A279790, A358830, A358836, A375136.
%K A375404 nonn
%O A375404 0,5
%A A375404 _Gus Wiseman_, Aug 17 2024