A118231 - OEIS

%I #11 Jun 13 2017 23:46:03

%S 1,-2,1,-2,0,1,4,-2,-2,1,-2,0,0,0,1,2,1,1,-2,-2,1,4,0,-2,0,-2,0,1,-6,

%T 1,6,-2,1,0,-2,1,-4,0,1,0,3,0,-2,0,1,6,-1,-6,4,-1,-2,4,-2,-2,1,-4,0,3,

%U 0,1,0,-2,0,0,0,1,4,0,-3,-1,-1,1,2,1,1,-2,-2,1,14,0,-7,0,-7,0,6,0,-2,0,-2,0,1,-14,0,3,1,10,0,-4,-2,3,0,1,0,-2,1

%N Triangle, read by rows, equal to the matrix square of triangle A118229.

%C Describes the sequence transformation of triangle A118229 iterated twice. Also equals the matrix inverse of triangle A118233.

%e Triangle begins:

%e 1;

%e -2, 1;

%e -2, 0, 1;

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

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

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

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

%e -6, 1, 6,-2, 1, 0,-2, 1;

%e -4, 0, 1, 0, 3, 0,-2, 0, 1;

%e 6,-1,-6, 4,-1,-2, 4,-2,-2, 1;

%e -4, 0, 3, 0, 1, 0,-2, 0, 0, 0, 1;

%e 4, 0,-3,-1,-1, 1, 2, 1, 1,-2,-2, 1;

%e 14, 0,-7, 0,-7, 0, 6, 0,-2, 0,-2, 0, 1; ...

%o (PARI) T(n,k)=if(n<k || k<0,0,(matrix(n,n,r,c,if(r>=c,if(gcd(r-c+1,c)==1,1,0)))^-2)[n,k])

%Y Cf. A118229, A118233 (inverse).

%K sign,tabl

%O 1,2

%A _Leroy Quet_, _Paul D. Hanna_, Apr 16 2006