A359042 - OEIS

A359042

Sum of partial sums of the n-th composition in standard order (A066099).

0, 1, 2, 3, 3, 5, 4, 6, 4, 7, 6, 9, 5, 8, 7, 10, 5, 9, 8, 12, 7, 11, 10, 14, 6, 10, 9, 13, 8, 12, 11, 15, 6, 11, 10, 15, 9, 14, 13, 18, 8, 13, 12, 17, 11, 16, 15, 20, 7, 12, 11, 16, 10, 15, 14, 19, 9, 14, 13, 18, 12, 17, 16, 21, 7, 13, 12, 18, 11, 17, 16, 22

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

LINKS

Table of n, a(n) for n=0..71.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

EXAMPLE

The 29th composition in standard order is (1,1,2,1), with partial sums (1,2,4,5), with sum 12, so a(29) = 12.

MATHEMATICA

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

Table[Total[Accumulate[stc[n]]], {n, 0, 100}]

CROSSREFS

See link for sequences related to standard compositions.

Each n appears A000009(n) times.

The reverse version is A029931.