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

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:
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;

Crossrefs

Cf. A000079, A000225, A001477, A011782, A001511, A001792, A195012, A209616, A228369, A228525, A228820.

Sequence in context: A113020 A347277 A357734 * A336932 A127258 A154557

Adjacent sequences: A228818 A228819 A228820 * A228822 A228823 A228824

Keyword

sign,tabf

Author

Omar E. Pol, Sep 05 2013

Status

approved