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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

%I #25 Sep 18 2013 12:31:55

%S 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,

%T -1,0,1,2,6,15,-5,-4,-4,-4,-4,-3,-3,-3,-3,-3,-3,-3,-2,-2,-2,-2,-2,-2,

%U -2,-1,-1,-1,-1,0,0,1,1,2,5,6,14,31,-6,-5,-5,-5,-5

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

%C 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.

%C Row sums is always 0.

%C Row lengths is A000079.

%C Column 1 is -1*A001477(n).

%C Right border gives A000225.

%C Row sums of nonnegative terms give A228820.

%e Triangle begins:

%e 0;

%e -1, 1;

%e -2, -1, 0, 3;

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

%e -4, -3, -3, -3, -2, -2, -2, -2, -1, -1, -1, 0, 1, 2, 6, 15;

%e -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;

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

%K sign,tabf

%O 1,4

%A _Omar E. Pol_, Sep 05 2013

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Last modified April 25 12:15 EDT 2024. Contains 371969 sequences. (Running on oeis4.)