A374758 - OEIS

A374758

Sum of leaders of strictly decreasing runs in the n-th composition in standard order.

0, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 5, 4, 3, 4, 5, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 5, 6, 5, 4, 5, 6, 3, 5, 5, 6, 5, 6, 5, 5, 4, 5, 5, 6, 5, 4, 5, 6, 5, 5, 5, 6, 5, 6, 5, 6, 5, 6, 6, 7, 6, 5, 6, 4, 4, 6, 6, 7, 6, 5, 4, 6, 5, 6, 6, 7, 6, 5, 6, 7, 6, 6

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OFFSET

0,3

COMMENTS

The leaders of strictly decreasing runs in a sequence are obtained by splitting it into maximal strictly decreasing subsequences and taking the first term of each.

LINKS

Table of n, a(n) for n=0..86.

Gus Wiseman, Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers.

EXAMPLE

The maximal strictly decreasing subsequences of the 1234567th composition in standard order are ((3,2,1),(2),(2,1),(2),(5,1),(1),(1)) with leaders (3,2,2,2,5,1,1), so a(1234567) = 16.

MATHEMATICA

stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;

Table[Total[First/@Split[stc[n], Greater]], {n, 0, 100}]

CROSSREFS

Row sums of A374757.

For leaders of constant runs we have A373953.

For leaders of anti-runs we have A374516.

For leaders of weakly increasing runs we have A374630.

For length instead of sum we have A124769.

The opposite version is A374684, sum of A374683 (length A124768).

The case of partitions ranked by Heinz numbers is A374706.

The weak version is A374741, sum of A374740 (length A124765).