cp's OEIS Frontend

A337698 Number of compositions of n that are not strictly increasing.

%I A337698 #7 Oct 13 2020 14:34:35
%S A337698 0,0,1,2,6,13,28,59,122,248,502,1012,2033,4078,8170,16357,32736,65498,
%T A337698 131026,262090,524224,1048500,2097063,4194200,8388486,16777074,
%U A337698 33554267,67108672,134217506,268435200,536870616,1073741484,2147483258,4294966848,8589934080
%N A337698 Number of compositions of n that are not strictly increasing.
%F A337698 a(n) = 2^(n-1) - A000009(n) for n > 0.
%e A337698 The a(2) = 1 through a(5) = 13 compositions:
%e A337698   (11)  (21)   (22)    (32)
%e A337698         (111)  (31)    (41)
%e A337698                (112)   (113)
%e A337698                (121)   (122)
%e A337698                (211)   (131)
%e A337698                (1111)  (212)
%e A337698                        (221)
%e A337698                        (311)
%e A337698                        (1112)
%e A337698                        (1121)
%e A337698                        (1211)
%e A337698                        (2111)
%e A337698                        (11111)
%t A337698 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!Less@@#&]],{n,0,15}]
%Y A337698 A000009 counts the complement.
%Y A337698 A047967 is the unordered version.
%Y A337698 A056823 is the weak version.
%Y A337698 A140106 counts the unordered case of length 3.
%Y A337698 A242771 counts the case of length 3.
%Y A337698 A333255 is the complement of a ranking sequence (using standard compositions A066099) for these compositions.
%Y A337698 A337481 counts these compositions that are not strictly decreasing.
%Y A337698 A337482 counts these compositions that are not weakly decreasing.
%Y A337698 A001523 counts unimodal compositions, with complement A115981.
%Y A337698 A007318 and A097805 count compositions by length.
%Y A337698 A218004 counts strictly increasing or weakly decreasing compositions.
%Y A337698 Cf. A000212, A128422, A332745, A332834, A332835, A337484.
%K A337698 nonn
%O A337698 0,4
%A A337698 _Gus Wiseman_, Oct 06 2020