1,8

The limit of the columns (without leading zeros) is A117166,

the Shift-Moebius transform of [1,0,0,0,...] (cf. A117165).

Column k+1 equals the Moebius transform of column k preceded by a zero,

where column k includes the k-1 zeros above the diagonal, for k>=1,

starting with A008683 in column 1.

Column 1 equals A008683 = Moebius transform of [1,0,0,0,...].

Column 2 = Moebius transform of column 1 preceded by a zero:

[0,1,-1,-2,0,-1,1,0,...] = Moebius([0,

1,-1,-1,0,-1,1,-1,...]).

Column 3 = Moebius transform of column 2 preceded by a zero:

[0,0,1,-1,-2,-1,-1,2,...] = Moebius([0,

0,1,-1,-2,0,-1,1,...]).

Column 4 = Moebius transform of column 3 preceded by a zero:

[0,0,0,1,-1,-2,-1,-2,...] = Moebius([0,

0,0,1,-1,-2,-1,-1,...]).

Triangle begins:

1;

-1, 1;

-1,-1, 1;

0,-2,-1, 1;

-1, 0,-2,-1, 1;

1,-1,-1,-2,-1, 1;

-1, 1,-1,-1,-2,-1, 1;

0, 0, 2,-2,-1,-2,-1, 1;

0, 1,-1, 2,-2,-1,-2,-1, 1;

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

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

0, 2, 2, 0, 4,-1, 1,-2,-1,-2,-1, 1;

-1, 0, 2, 2, 0, 4,-1, 1,-2,-1,-2,-1, 1; ...

Cf. A112682 (inverse), A008683 (column 1), A117163 (column 2), A117164 (column 3); A117165 (Shift-Moebius), A117170 (inverse Shift-Moebius).

Sequence in context: A135997 A026609 A090340 this_sequence A146061 A135936 A109707

Adjacent sequences: A117159 A117160 A117161 this_sequence A117163 A117164 A117165

sign,tabl

Wouter Meeussen (wouter.meeussen(AT)pandora.be) and Paul D. Hanna (pauldhanna(AT)juno.com), Mar 05 2006