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A332875
Sizes of maximal weakly increasing subsequences of A000002.
8
3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 4, 3, 3, 3, 2, 4, 3, 2, 3, 4, 3, 3, 3, 2, 3, 4, 2, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 3, 4, 2, 3, 4, 3
OFFSET
1,1
FORMULA
a(n) = A000002(2*n - 1) + A000002(2*n).
EXAMPLE
The weakly increasing 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).
MATHEMATICA
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&]
CROSSREFS
The number of runs in the first n terms of A000002 is A156253.
The weakly decreasing version is A332273.
Sequence in context: A334625 A209291 A375642 * A176873 A227727 A050499
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 08 2020
STATUS
approved