A118233 Triangle, read by rows, equal to the matrix square of triangle A054431.

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, 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, 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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..104.

Formula

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.

Example

Triangle begins:
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, 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, 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, 1; ...
where column 1 forms Euler totient function phi(n).

Prog

(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]}

Crossrefs

Cf. A054431, A118231 (matrix inverse).

Sequence in context: A129680 A118231 A166453 * A255273 A181117 A245472

Adjacent sequences: A118230 A118231 A118232 * A118234 A118235 A118236

Keyword

nonn,tabl

Author

Leroy Quet, Paul D. Hanna, Apr 16 2006

Status

approved