A117162 Matrix inverse of triangle A112682.

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

Offset

1,8

Comments

The limit of the columns (without leading zeros) is A117166, the Shift-Moebius transform of [1,0,0,0,...] (cf. A117165).

Links

Table of n, a(n) for n=1..91.

Formula

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.

Example

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; ...

Crossrefs

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

Sequence in context: A090340 A287364 A340676 * A277045 A146061 A331186

Adjacent sequences: A117159 A117160 A117161 * A117163 A117164 A117165

Keyword

sign,tabl

Author

Wouter Meeussen and Paul D. Hanna, Mar 05 2006

Status

approved