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A117162 Matrix inverse of triangle A112682. 4

%I #9 May 31 2013 18:56:20

%S 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,

%T -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,

%U -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

%N Matrix inverse of triangle A112682.

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

%F 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.

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

%e 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,...]).

%e 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,...]).

%e 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,...]).

%e Triangle begins:

%e 1;

%e -1, 1;

%e -1,-1, 1;

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

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

%e 1,-1,-1,-2,-1, 1;

%e -1, 1,-1,-1,-2,-1, 1;

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

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

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

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

%e 0, 2, 2, 0, 4,-1, 1,-2,-1,-2,-1, 1;

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

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

%K sign,tabl

%O 1,8

%A _Wouter Meeussen_ and _Paul D. Hanna_, Mar 05 2006

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)