This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337481 #11 Sep 17 2020 20:32:27
%S A337481 0,0,1,1,5,11,25,55,117,241,493,1001,2019,4061,8149,16331,32705,65461,
%T A337481 130981,262037,524161,1048425,2096975,4194097,8388365,16776933,
%U A337481 33554103,67108481,134217285,268434945,536870321,1073741145,2147482869,4294966401,8589933569
%N A337481 Number of compositions of n that are neither strictly increasing nor strictly decreasing.
%C A337481 A composition of n is a finite sequence of positive integers summing to n.
%F A337481 a(n) = 2^(n-1) - 2*A000009(n) + 1, n > 0.
%e A337481 The a(2) = 1 through a(5) = 11 compositions:
%e A337481 (11) (111) (22) (113)
%e A337481 (112) (122)
%e A337481 (121) (131)
%e A337481 (211) (212)
%e A337481 (1111) (221)
%e A337481 (311)
%e A337481 (1112)
%e A337481 (1121)
%e A337481 (1211)
%e A337481 (2111)
%e A337481 (11111)
%t A337481 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!Less@@#&&!Greater@@#&]],{n,0,15}]
%Y A337481 Ranked by the complement of the intersection of A333255 and A333256.
%Y A337481 A332834 is the weak version.
%Y A337481 A337482 is the semi-strict version.
%Y A337481 A337484 counts only compositions of length 3.
%Y A337481 A007318 and A097805 count compositions by length.
%Y A337481 A032020 counts strict compositions, ranked by A233564.
%Y A337481 A218004 counts strictly increasing or weakly decreasing compositions.
%Y A337481 Cf. A216652, A329398, A337462, A337483, A337605.
%K A337481 nonn
%O A337481 0,5
%A A337481 _Gus Wiseman_, Sep 11 2020