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 A353860 #10 Feb 04 2023 14:15:14
%S A353860 0,1,2,2,5,2,12,2,26,9,36,2,206,2,132,40,677,2,1746,2,3398,136,2052,2,
%T A353860 44388,33,8196,730,79166,2,263234,2,458330,2056,131076,160,8804349,2,
%U A353860 524292,8200,13662156,2,36036674,2,48844526,90282,8388612,2,1971667502,129
%N A353860 Number of collapsible integer compositions of n.
%C A353860 If a collapse is a joining of some number of adjacent equal parts of an integer composition, we call a composition collapsible iff by some sequence of collapses it can be reduced to a single part. An example of such a sequence of collapses is (1,1,1,3,2,1,1,2) -> (3,3,2,1,1,2) -> (3,3,2,2,2) -> (6,2,2,2) -> (6,6) -> (12), which shows that (1,1,1,3,2,1,1,2) is a collapsible composition of 12.
%H A353860 Andrew Howroyd, <a href="/A353860/b353860.txt">Table of n, a(n) for n = 0..1000</a>
%F A353860 Sum_{d|n} mu(d)*a(n/d)^d = 1 for n > 0. - _Andrew Howroyd_, Feb 04 2023
%e A353860 The a(0) = 0 through a(6) = 12 compositions:
%e A353860 . (1) (2) (3) (4) (5) (6)
%e A353860 (11) (111) (22) (11111) (33)
%e A353860 (112) (222)
%e A353860 (211) (1113)
%e A353860 (1111) (1122)
%e A353860 (2112)
%e A353860 (2211)
%e A353860 (3111)
%e A353860 (11112)
%e A353860 (11211)
%e A353860 (21111)
%e A353860 (111111)
%t A353860 repcams[q_List]:=repcams[q]=Union[{q},If[UnsameQ@@q,{},Union@@repcams/@ Union[Insert[Drop[q,#],Plus@@Take[q,#],First[#]]&/@ Select[Tuples[Range[Length[q]],2],And[Less@@#,SameQ@@Take[q,#]]&]]]];
%t A353860 Table[Length[Select[Join@@Permutations/@ IntegerPartitions[n],MemberQ[repcams[#],{n}]&]],{n,0,15}]
%o A353860 (PARI) a(n) = if(n==0, 0, 1 - sumdiv(n, d, if(d>1, moebius(d)*a(n/d)^d ))) \\ _Andrew Howroyd_, Feb 04 2023
%Y A353860 The version for partitions is A275870, ranked by A300273.
%Y A353860 A003242 counts anti-run compositions, ranked by A333489, complement A261983.
%Y A353860 A011782 counts compositions.
%Y A353860 A353847 represents the run-sums of a composition, partitions A353832.
%Y A353860 A353853-A353859 pertain to composition run-sum trajectory.
%Y A353860 A353932 lists run-sums of standard compositions.
%Y A353860 Cf. A237685, A238279, A304442, A318928, A333755, A353844, A353848, A353849, A353850, A353852.
%K A353860 nonn
%O A353860 0,3
%A A353860 _Gus Wiseman_, Jun 04 2022
%E A353860 Terms a(16) and beyond from _Andrew Howroyd_, Feb 04 2023