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 A332274 #8 Feb 14 2020 08:02:31
%S A332274 1,1,2,4,7,11,22,33,56,93,162,264,454,765,1307,2237,3849,6611,11472,
%T A332274 19831,34446,59865,104293,181561,316924
%N A332274 Number of totally strong compositions of n.
%C A332274 A sequence is totally strong if either it is empty, equal to (1), or its run-lengths are weakly decreasing (strong) and are themselves a totally strong sequence.
%C A332274 A composition of n is a finite sequence of positive integers with sum n.
%C A332274 Also the number of totally co-strong compositions of n.
%e A332274 The a(1) = 1 through a(5) = 11 compositions:
%e A332274 (1) (2) (3) (4) (5)
%e A332274 (11) (12) (13) (14)
%e A332274 (21) (22) (23)
%e A332274 (111) (31) (32)
%e A332274 (121) (41)
%e A332274 (211) (122)
%e A332274 (1111) (131)
%e A332274 (212)
%e A332274 (311)
%e A332274 (2111)
%e A332274 (11111)
%t A332274 tni[q_]:=Or[q=={},q=={1},And[GreaterEqual@@Length/@Split[q],tni[Length/@Split[q]]]];
%t A332274 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],tni]],{n,0,15}]
%Y A332274 The case of partitions is A316496.
%Y A332274 The co-strong case is A332274 (this sequence).
%Y A332274 The case of reversed partitions is A332275.
%Y A332274 The alternating version is A332338.
%Y A332274 Cf. A100883, A107429, A317245, A317256, A317491, A329744, A332272, A332279, A332289, A332292, A332336, A332337, A332339, A332340.
%K A332274 nonn,more
%O A332274 0,3
%A A332274 _Gus Wiseman_, Feb 11 2020