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 A329749 #7 Jul 06 2020 19:56:22
%S A329749 1,1,0,2,3,5,11,23,40,80,180,344,661,1321,2657,5268,10481,20903,41572,
%T A329749 82734,164998,328304,654510,1305421,2598811,5182174,10332978,20594318,
%U A329749 41066611,81897091,163309679,325707492,649648912,1295827380,2584941276,5156774487
%N A329749 Number of complete compositions of n whose run-lengths cover an initial interval of positive integers.
%C A329749 A composition of n is a finite sequence of positive integers with sum n. It is complete if it covers an initial interval of positive integers.
%e A329749 The a(0) = 1 through a(6) = 11 compositions (empty column not shown):
%e A329749 () (1) (1,2) (1,1,2) (1,2,2) (1,2,3)
%e A329749 (2,1) (1,2,1) (2,1,2) (1,3,2)
%e A329749 (2,1,1) (2,2,1) (2,1,3)
%e A329749 (1,1,2,1) (2,3,1)
%e A329749 (1,2,1,1) (3,1,2)
%e A329749 (3,2,1)
%e A329749 (1,2,1,2)
%e A329749 (1,2,2,1)
%e A329749 (2,1,1,2)
%e A329749 (2,1,2,1)
%e A329749 (1,1,2,1,1)
%t A329749 normQ[m_]:=Or[m=={},Union[m]==Range[Max[m]]];
%t A329749 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],normQ[#]&&normQ[Length/@Split[#]]&]],{n,0,10}]
%Y A329749 Looking at multiplicities instead of run-lengths gives A329748.
%Y A329749 The non-complete version is A329766.
%Y A329749 Complete compositions are A107429.
%Y A329749 Cf. A000740, A008965, A098504, A244164, A274174, A329738, A329739, A329740, A329741, A329744.
%K A329749 nonn
%O A329749 0,4
%A A329749 _Gus Wiseman_, Nov 21 2019
%E A329749 a(21)-a(35) from _Alois P. Heinz_, Jul 06 2020