A228821 - OEIS

A228821

Triangle read by rows in which row n lists the F-ranks of all compositions of n in nondecreasing order, n >= 0.

0, -1, 1, -2, -1, 0, 3, -3, -2, -2, -1, -1, 0, 2, 7, -4, -3, -3, -3, -2, -2, -2, -2, -1, -1, -1, 0, 1, 2, 6, 15, -5, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, 0, 0, 1, 1, 2, 5, 6, 14, 31, -6, -5, -5, -5, -5

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

OFFSET

1,4

COMMENTS

Also row n lists the L-ranks of all compositions of n in nondecreasing order. For the definition of both F-rank and L-rank of a composition see A228820.

Row sums is always 0.

Row lengths is A000079.

Column 1 is -1*A001477(n).

Right border gives A000225.

Row sums of nonnegative terms give A228820.

LINKS

Table of n, a(n) for n=1..68.

EXAMPLE

Triangle begins:

-1, 1;

-2, -1, 0, 3;

-3, -2, -2, -1, -1, 0, 2, 7;