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A228821
Triangle read by rows in which row n lists the F-ranks of all compositions of n in nondecreasing order, n >= 0.
1
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
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.
EXAMPLE
Triangle begins:
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;
KEYWORD
sign,tabf
AUTHOR
Omar E. Pol, Sep 05 2013
STATUS
approved