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 A330028 #8 Nov 28 2019 08:07:10
%S A330028 1,1,2,3,7,13,23,45,86,159,303,568,1069,2005,3769,7066,13251,24821,
%T A330028 46482,86988,162758
%N A330028 Number of compositions of n with cuts-resistance <= 2.
%C A330028 A composition of n is a finite sequence of positive integers summing to n.
%C A330028 For the operation of shortening all runs by 1, cuts-resistance is defined to be the number of applications required to reach an empty word.
%e A330028 The a(0) = 1 through a(5) = 13 compositions:
%e A330028 () (1) (2) (3) (4) (5)
%e A330028 (1,1) (1,2) (1,3) (1,4)
%e A330028 (2,1) (2,2) (2,3)
%e A330028 (3,1) (3,2)
%e A330028 (1,1,2) (4,1)
%e A330028 (1,2,1) (1,1,3)
%e A330028 (2,1,1) (1,2,2)
%e A330028 (1,3,1)
%e A330028 (2,1,2)
%e A330028 (2,2,1)
%e A330028 (3,1,1)
%e A330028 (1,1,2,1)
%e A330028 (1,2,1,1)
%t A330028 degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&,q,Length[#]>0&]]-1;
%t A330028 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],degdep[#]<=2&]],{n,0,10}]
%Y A330028 Sum of first three columns of A329861.
%Y A330028 Compositions with cuts-resistance 1 are A003242.
%Y A330028 Compositions with cuts-resistance 2 are A329863.
%Y A330028 Compositions with runs-resistance 2 are A329745.
%Y A330028 Numbers whose binary expansion has cuts-resistance 2 are A329862.
%Y A330028 Binary words with cuts-resistance 2 are A027383.
%Y A330028 Cuts-resistance of binary expansion is A319416.
%Y A330028 Binary words counted by cuts-resistance are A319421 or A329860.
%Y A330028 Cf. A000975, A003242, A032020, A114901, A240085, A261983, A319420, A329738, A329744, A329864.
%K A330028 nonn,more
%O A330028 0,3
%A A330028 _Gus Wiseman_, Nov 27 2019