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 A330028 Number of compositions of n with cuts-resistance <= 2. 1
 1, 1, 2, 3, 7, 13, 23, 45, 86, 159, 303, 568, 1069, 2005, 3769, 7066, 13251, 24821, 46482, 86988, 162758 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A composition of n is a finite sequence of positive integers summing to n. 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. LINKS EXAMPLE The a(0) = 1 through a(5) = 13 compositions:   ()  (1)  (2)    (3)    (4)      (5)            (1,1)  (1,2)  (1,3)    (1,4)                   (2,1)  (2,2)    (2,3)                          (3,1)    (3,2)                          (1,1,2)  (4,1)                          (1,2,1)  (1,1,3)                          (2,1,1)  (1,2,2)                                   (1,3,1)                                   (2,1,2)                                   (2,2,1)                                   (3,1,1)                                   (1,1,2,1)                                   (1,2,1,1) MATHEMATICA degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&, q, Length[#]>0&]]-1; Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], degdep[#]<=2&]], {n, 0, 10}] CROSSREFS Sum of first three columns of A329861. Compositions with cuts-resistance 1 are A003242. Compositions with cuts-resistance 2 are A329863. Compositions with runs-resistance 2 are A329745. Numbers whose binary expansion has cuts-resistance 2 are A329862. Binary words with cuts-resistance 2 are A027383. Cuts-resistance of binary expansion is A319416. Binary words counted by cuts-resistance are A319421 or A329860. Cf. A000975, A003242, A032020, A114901, A240085, A261983, A319420, A329738, A329744, A329864. Sequence in context: A298339 A091440 A175211 * A075058 A213968 A213967 Adjacent sequences:  A330025 A330026 A330027 * A330029 A330030 A330031 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 27 2019 STATUS approved

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Last modified September 20 12:13 EDT 2020. Contains 337264 sequences. (Running on oeis4.)