A118233 - OEIS

%I #8 Mar 11 2014 01:32:18

%S 1,2,1,2,0,1,4,2,2,1,2,0,0,0,1,6,3,3,2,2,1,4,0,2,0,2,0,1,6,3,2,2,3,0,

%T 2,1,4,0,3,0,1,0,2,0,1,10,5,6,4,5,2,4,2,2,1,4,0,1,0,3,0,2,0,0,0,1,12,

%U 6,7,5,7,3,6,3,3,2,2,1,6,0,3,0,3,0,2,0,2,0,2,0,1,8,4,3,3,4,0,4,2,1,0,3,0,2

%N Triangle, read by rows, equal to the matrix square of triangle A054431.

%C Describes the sequence transformation of triangle A054431 iterated twice. Also, equals the matrix inverse of triangle A118231.

%F Column 1: T(n,1) = phi(n). Column 2: T(2*n-1,2) = 0; T(2*n,2) = phi(2*n+1)/2. Column 3: T(3*n-1) = phi(3*n)/2 - 1. Column 4: T(2*n-1,4) = 0; T(2*n,4) = phi(2*n+1)/2 - 1.

%e Triangle begins:

%e 1;

%e 2, 1;

%e 2, 0, 1;

%e 4, 2, 2, 1;

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

%e 6, 3, 3, 2, 2, 1;

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

%e 6, 3, 2, 2, 3, 0, 2, 1;

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

%e 10, 5, 6, 4, 5, 2, 4, 2, 2, 1;

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

%e 12, 6, 7, 5, 7, 3, 6, 3, 3, 2, 2, 1;

%e 6, 0, 3, 0, 3, 0, 2, 0, 2, 0, 2, 0, 1;

%e 8, 4, 3, 3, 4, 0, 4, 2, 1, 0, 3, 0, 2, 1; ...

%e where column 1 forms Euler totient function phi(n).

%o (PARI) {T(n,k)=local(M=matrix(n,n,r,c,if(r>=c,if(gcd(r-c+1,c)==1,1,0)))^2);M[n,k]}

%Y Cf. A054431, A118231 (matrix inverse).

%K nonn,tabl

%O 1,2

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