A332875 Sizes of maximal weakly increasing subsequences of A000002.

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

Links

Table of n, a(n) for n=1..87.

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.

Cf. A000002, A001462, A013947, A013948, A088568, A288605, A296658, A329315, A329316, A329317, A329362.

Sequence in context: A365458 A334625 A209291 * A176873 A227727 A050499

Adjacent sequences: A332872 A332873 A332874 * A332876 A332877 A332878

Keyword

nonn

Author

Gus Wiseman, Mar 08 2020

Status

approved