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Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n.
1

%I #2 Mar 31 2012 20:25:00

%S 1,-1,2,-1,0,3,0,-2,0,2,-1,0,0,0,5,1,-2,-3,0,0,2,-1,0,0,0,0,0,7,0,0,0,

%T -2,0,0,0,2,0,0,-3,0,0,0,0,0,3,1,-2,0,0,-5,0,0,0,0,2,-1,0,0,0,0,0,0,0,

%U 0,0,11,0,2,0,-2,0,-2,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,13,1,-2,0,0,0,0,-7,0,0,0,0,0,0,2

%N Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n.

%C Right border = A020639, Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...).

%C Left border = mu(n), A008683: (1, -1, -1, 0, -1, 1, -1,...).

%C Row sums = a signed version of A097945: (1, -1, -2, 0, -4, 2, -6,...) such that parity = (+) iff mu(n) = +.

%F Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n; where A020639 = Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2,...) and A054525 = the Mobius transform.

%e First few rows of the triangle =

%e 1;

%e -1, 2;

%e -1, 0, 3;

%e 0, -2, 0, 2;

%e -1, 0, 0, 0, 5;

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

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

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

%e 0, 0, -3, 0, 0, 0, 0, 0, 3;

%e 1, -2, 0, 0, -5, 0, 0, 0, 0, 2;

%e -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11;

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

%e ...

%Y Cf. A008683, A097945, A020639, A054525.

%K tabl,sign

%O 1,3

%A Gary W. Adamson & _Mats Granvik_, Jul 27 2008