%I A118233
%S A118233 1,2,1,2,0,1,4,2,2,1,2,0,0,0,1,6,3,3,2,2,1,4,0,2,0,2,0,1,6,3,2,2,3,0,2,
%T A118233 1,4,0,3,0,1,0,2,0,1,10,5,6,4,5,2,4,2,2,1,4,0,1,0,3,0,2,0,0,0,1,12,6,7,
%U A118233 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 A118233 Triangle, read by rows, equal to the matrix square of triangle A054431.
%C A118233 Describes the sequence transformation of triangle A054431 iterated twice. 
               Also, equals the matrix inverse of triangle A118231.
%H A118233 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A118233 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 A118233 Triangle begins:
%e A118233 1;
%e A118233 2, 1;
%e A118233 2, 0, 1;
%e A118233 4, 2, 2, 1;
%e A118233 2, 0, 0, 0, 1;
%e A118233 6, 3, 3, 2, 2, 1;
%e A118233 4, 0, 2, 0, 2, 0, 1;
%e A118233 6, 3, 2, 2, 3, 0, 2, 1;
%e A118233 4, 0, 3, 0, 1, 0, 2, 0, 1;
%e A118233 10, 5, 6, 4, 5, 2, 4, 2, 2, 1;
%e A118233 4, 0, 1, 0, 3, 0, 2, 0, 0, 0, 1;
%e A118233 12, 6, 7, 5, 7, 3, 6, 3, 3, 2, 2, 1;
%e A118233 6, 0, 3, 0, 3, 0, 2, 0, 2, 0, 2, 0, 1;
%e A118233 8, 4, 3, 3, 4, 0, 4, 2, 1, 0, 3, 0, 2, 1; ...
%e A118233 where column 1 forms Euler totient function phi(n).
%o A118233 (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 A118233 Cf. A054431, A118231 (matrix inverse).
%Y A118233 Sequence in context: A129680 A118231 A166453 this_sequence A159955 A053838 
               A117167
%Y A118233 Adjacent sequences: A118230 A118231 A118232 this_sequence A118234 A118235 
               A118236
%K A118233 nonn,tabl
%O A118233 1,2
%A A118233 Leroy Quet, Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2006