A382288 - OEIS

A382288

Number of records in the n-th composition in standard order.

0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1

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

OFFSET

0,7

COMMENTS

Here a record is a part of the composition that is greater than all parts before it, reading left to right. The first part of any nonempty composition is a record so a(n) >= 1 for n > 0. See A066099 for the standard order of integer compositions.

The first appearance of k occurs at n = A164894(k) for k > 0.

LINKS

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

FORMULA

a(A164894(n)) = n for n > 0.

EXAMPLE

The 883rd composition is (1, 2, 1, 1, 3, 1, 1) with records 1, 2, and 3; so a(883) = 3.

^ ^ ^

PROG

(Python)

def comp(n):

return # see A357625