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A332273
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Sizes of maximal weakly decreasing subsequences of A000002.
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7
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1, 4, 2, 3, 4, 3, 3, 3, 2, 4, 3, 2, 3, 4, 2, 3, 3, 3, 3, 4, 2, 3, 4, 3, 2, 3, 3, 3, 4, 2, 3, 4, 3, 3, 3, 2, 3, 4, 3, 2, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 2, 4, 3, 2, 3, 3, 3, 4, 2, 3, 4, 3, 2, 4, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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The weakly decreasing subsequences begin: (1), (2,2,1,1), (2,1), (2,2,1), (2,2,1,1), (2,1,1), (2,2,1), (2,1,1), (2,1), (2,2,1,1), (2,1,1), (2,1), (2,2,1), (2,2,1,1).
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MATHEMATICA
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kolagrow[q_]:=If[Length[q]<2, Take[{1, 2}, Length[q]+1], Append[q, Switch[{q[[Length[Split[q]]]], q[[-2]], Last[q]}, {1, 1, 1}, 0, {1, 1, 2}, 1, {1, 2, 1}, 2, {1, 2, 2}, 0, {2, 1, 1}, 2, {2, 1, 2}, 2, {2, 2, 1}, 1, {2, 2, 2}, 1]]]
kol[n_Integer]:=Nest[kolagrow, {1}, n-1];
Length/@Split[kol[40], #1>=#2&]
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CROSSREFS
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The weakly increasing version is A332875.
Cf. A000002, A001462, A013947, A013948, A088568, A288605, A296658, A329315, A329316, A329317, A329362.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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