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 A356604 #10 Sep 01 2022 19:48:14
%S A356604 1,1,1,1,3,4,5,9,13,24,40,61,101,160,257,415,679,1103,1774,2884,4656,
%T A356604 7517,12165,19653,31753,51390,83134,134412,217505,351814,569081,
%U A356604 920769,1489587,2409992,3899347,6309059,10208628,16518910,26729830,43254212,69994082
%N A356604 Number of integer compositions of n into odd parts covering an initial interval of odd positive integers.
%e A356604 The a(1) = 1 through a(8) = 13 compositions:
%e A356604 (1) (11) (111) (13) (113) (1113) (133) (1133)
%e A356604 (31) (131) (1131) (313) (1313)
%e A356604 (1111) (311) (1311) (331) (1331)
%e A356604 (11111) (3111) (11113) (3113)
%e A356604 (111111) (11131) (3131)
%e A356604 (11311) (3311)
%e A356604 (13111) (111113)
%e A356604 (31111) (111131)
%e A356604 (1111111) (111311)
%e A356604 (113111)
%e A356604 (131111)
%e A356604 (311111)
%e A356604 (11111111)
%e A356604 The a(9) = 24 compositions:
%e A356604 (135) (11133) (1111113) (111111111)
%e A356604 (153) (11313) (1111131)
%e A356604 (315) (11331) (1111311)
%e A356604 (351) (13113) (1113111)
%e A356604 (513) (13131) (1131111)
%e A356604 (531) (13311) (1311111)
%e A356604 (31113) (3111111)
%e A356604 (31131)
%e A356604 (31311)
%e A356604 (33111)
%t A356604 normQ[m_]:=Or[m=={},Union[m]==Range[Max[m]]];
%t A356604 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],normQ[(#+1)/2]&]],{n,0,15}]
%Y A356604 The case of partitions is A053251, ranked by A356232 and A356603.
%Y A356604 These compositions are ranked by the intersection of A060142 and A333217.
%Y A356604 This is the odd initial case of A107428.
%Y A356604 This is the odd restriction of A107429.
%Y A356604 This is the normal/covering case of A324969 (essentially A000045).
%Y A356604 The non-initial version is A356605.
%Y A356604 A000041 counts partitions, compositions A011782.
%Y A356604 A055932 lists numbers with prime indices covering an initial interval.
%Y A356604 A066208 lists numbers with all odd prime indices, counted by A000009.
%Y A356604 Cf. A001221, A001222, A001227, A005408, A061395, A066205, A073493, A137921, A356224.
%K A356604 nonn
%O A356604 0,5
%A A356604 _Gus Wiseman_, Aug 30 2022
%E A356604 More terms from _Alois P. Heinz_, Sep 01 2022