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Matrix inverse of Sierpinski's triangle (A047999, Pascal's triangle mod 2).
1

%I #5 Jun 06 2016 23:43:34

%S 1,-1,1,-1,0,1,1,-1,-1,1,-1,0,0,0,1,1,-1,0,0,-1,1,1,0,-1,0,-1,0,1,-1,

%T 1,1,-1,1,-1,-1,1,-1,0,0,0,0,0,0,0,1,1,-1,0,0,0,0,0,0,-1,1,1,0,-1,0,0,

%U 0,0,0,-1,0,1,-1,1,1,-1,0,0,0,0,1,-1,-1,1,1,0,0,0,-1,0,0,0,-1,0,0,0,1

%N Matrix inverse of Sierpinski's triangle (A047999, Pascal's triangle mod 2).

%C In absolute values equal to A047999. - _M. F. Hasler_, Jun 06 2016

%e Triangle begins:

%e 1,

%e -1, 1,

%e -1, 0, 1,

%e 1,-1,-1, 1,

%e -1, 0, 0, 0, 1,

%e 1,-1, 0, 0,-1, 1,

%e 1, 0,-1, 0,-1, 0, 1,

%e -1, 1, 1,-1, 1,-1,-1, 1,

%e -1, 0, 0, 0, 0, 0, 0, 0, 1,

%e 1,-1, 0, 0, 0, 0, 0, 0,-1, 1,

%e 1, 0,-1, 0, 0, 0, 0, 0,-1, 0, 1,

%e -1, 1, 1,-1, 0, 0, 0, 0, 1,-1,-1, 1,

%e 1, 0, 0, 0,-1, 0, 0, 0,-1, 0, 0, 0, 1,

%e ...

%o (PARI) p=2; s=13; P=matpascal(s); PM=matrix(s+1,s+1,n,k,P[n,k]%p); IPM = 1/PM;

%o for(n=1,s,for(k=1,n,print1(IPM[n,k],","));print())

%Y Cf. A007318, A047999.

%K easy,sign,tabl

%O 0,1

%A _Gerald McGarvey_, Oct 10 2009