cp's OEIS Frontend

A337482 Number of compositions of n that are neither strictly increasing nor weakly decreasing.

%I A337482 #10 Sep 17 2020 20:32:38
%S A337482 0,0,0,0,2,7,18,45,101,219,461,957,1957,3978,8036,16182,32506,65202,
%T A337482 130642,261601,523598,1047709,2096062,4192946,8386912,16775117,
%U A337482 33551832,67105663,134213789,268430636,536865013,1073734643,2147474910,4294956706,8589921771
%N A337482 Number of compositions of n that are neither strictly increasing nor weakly decreasing.
%C A337482 A composition of n is a finite sequence of positive integers summing to n.
%F A337482 a(n) = 2^(n-1) - A000009(n) - A000041(n) + 1, n > 0.
%e A337482 The a(4) = 2 through a(4) = 18 compositions:
%e A337482   (112)  (113)   (114)
%e A337482   (121)  (122)   (132)
%e A337482          (131)   (141)
%e A337482          (212)   (213)
%e A337482          (1112)  (231)
%e A337482          (1121)  (312)
%e A337482          (1211)  (1113)
%e A337482                  (1122)
%e A337482                  (1131)
%e A337482                  (1212)
%e A337482                  (1221)
%e A337482                  (1311)
%e A337482                  (2112)
%e A337482                  (2121)
%e A337482                  (11112)
%e A337482                  (11121)
%e A337482                  (11211)
%e A337482                  (12111)
%t A337482 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!Less@@#&&!GreaterEqual@@#&]],{n,0,15}]
%Y A337482 Ranked by the complement of the intersection of A114994 and A333255.
%Y A337482 A128422 counts only the case of length 3.
%Y A337482 A218004 counts the complement.
%Y A337482 A332834 is the weak version.
%Y A337482 A337481 is the strict version.
%Y A337482 A001523 counts unimodal compositions, with complement counted by A115981.
%Y A337482 A007318 and A097805 count compositions by length.
%Y A337482 A032020 counts strict compositions, ranked by A233564.
%Y A337482 A332745/A332835 count partitions/compositions with weakly increasing or weakly decreasing run-lengths.
%Y A337482 Cf. A216652, A329398, A332831, A332833, A337462, A337483, A337484, A337605.
%K A337482 nonn
%O A337482 0,5
%A A337482 _Gus Wiseman_, Sep 11 2020