cp's OEIS Frontend

A374679 Number of integer compositions of n whose leaders of anti-runs are strictly increasing.

%I A374679 #9 Sep 16 2024 08:42:44
%S A374679 1,1,1,3,4,8,15,24,45,84,142,256,464,817,1464,2621,4649,8299,14819,
%T A374679 26389,47033,83833,149325,266011,473867,843853
%N A374679 Number of integer compositions of n whose leaders of anti-runs are strictly increasing.
%C A374679 The leaders of anti-runs in a sequence are obtained by splitting it into maximal consecutive anti-runs (sequences with no adjacent equal terms) and taking the first term of each.
%H A374679 Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.
%e A374679 The a(0) = 1 through a(6) = 15 compositions:
%e A374679   ()  (1)  (2)  (3)   (4)    (5)    (6)
%e A374679                 (12)  (13)   (14)   (15)
%e A374679                 (21)  (31)   (23)   (24)
%e A374679                       (121)  (32)   (42)
%e A374679                              (41)   (51)
%e A374679                              (122)  (123)
%e A374679                              (131)  (132)
%e A374679                              (212)  (141)
%e A374679                                     (213)
%e A374679                                     (231)
%e A374679                                     (312)
%e A374679                                     (321)
%e A374679                                     (1212)
%e A374679                                     (1221)
%e A374679                                     (2121)
%t A374679 Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n],Less@@First/@Split[#,UnsameQ]&]],{n,0,15}]
%Y A374679 For distinct but not necessarily increasing leaders we have A374518.
%Y A374679 For partitions instead of compositions we have A375134.
%Y A374679 Other types of runs (instead of anti-):
%Y A374679 - For leaders of identical runs we have A000041.
%Y A374679 - For leaders of weakly increasing runs we have A374634.
%Y A374679 - For leaders of strictly increasing runs we have A374688.
%Y A374679 - For leaders of strictly decreasing runs we have A374762.
%Y A374679 Other types of run-leaders (instead of strictly increasing):
%Y A374679 - For identical leaders we have A374517.
%Y A374679 - For distinct leaders we have A374518.
%Y A374679 - For weakly increasing leaders we have A374681.
%Y A374679 - For weakly decreasing leaders we have A374682.
%Y A374679 - For strictly decreasing leaders we have A374680.
%Y A374679 A003242 counts anti-runs, ranks A333489.
%Y A374679 A106356 counts compositions by number of maximal anti-runs.
%Y A374679 A238279 counts compositions by number of maximal runs.
%Y A374679 A238424 counts partitions whose first differences are an anti-run.
%Y A374679 A274174 counts contiguous compositions, ranks A374249.
%Y A374679 Cf. A188920, A238343, A333213, A333381, A373949, A374515, A374632, A374635, A374678, A374700, A374706, A375133.
%K A374679 nonn,more
%O A374679 0,4
%A A374679 _Gus Wiseman_, Aug 01 2024