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 A356846 #8 Sep 03 2022 12:19:49
%S A356846 0,0,0,0,2,5,11,25,57,115,236,482,978,1986,4003,8033,16150,32402,
%T A356846 64943,130207,260805,522123,1045168,2091722,4185431,8374100,16753538,
%U A356846 33515122,67042865,134106640,268246886,536549760,1073194999,2146553011,4293391411,8587283895
%N A356846 Number of integer compositions of n into parts not covering an interval of positive integers.
%F A356846 a(n) = A011782(n) - A107428(n).
%e A356846 The a(0) = 0 through a(6) = 8 compositions:
%e A356846 . . . . (13) (14) (15)
%e A356846 (31) (41) (24)
%e A356846 (113) (42)
%e A356846 (131) (51)
%e A356846 (311) (114)
%e A356846 (141)
%e A356846 (411)
%e A356846 (1113)
%e A356846 (1131)
%e A356846 (1311)
%e A356846 (3111)
%t A356846 gappyQ[m_]:=And[m!={},Union[m]!=Range[Min[m],Max[m]]];
%t A356846 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],gappyQ]],{n,0,15}]
%Y A356846 The complement is counted by A107428, initial A107429.
%Y A356846 The case of partitions is A239955, ranked by A073492, initial A053251, complement A034296.
%Y A356846 These compositions are ranked by A356842, complement A356841.
%Y A356846 A000041 counts partitions, compositions A011782.
%Y A356846 A066208 lists numbers with all odd prime indices, counted by A000009.
%Y A356846 A073491 lists numbers with gapless prime indices, initial A055932.
%Y A356846 Cf. A001227, A060142, A080259, A188575, A239327, A356604, A356605.
%K A356846 nonn
%O A356846 0,5
%A A356846 _Gus Wiseman_, Sep 03 2022