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A117162
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Matrix inverse of triangle A112682.
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4
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| The limit of the columns (without leading zeros) is A117166,
the Shift-Moebius transform of [1,0,0,0,...] (cf. A117165).
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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.
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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; ...
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CROSSREFS
| 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 * A146061 A135936 A109707
Adjacent sequences: A117159 A117160 A117161 * A117163 A117164 A117165
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KEYWORD
| sign,tabl
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be) and Paul D. Hanna (pauldhanna(AT)juno.com), Mar 05 2006
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