A118231 Triangle, read by rows, equal to the matrix square of triangle A118229.

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, 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, 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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..105.

Example

Triangle begins:
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, 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, 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; ...

Prog

(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])

Crossrefs

Cf. A118229, A118233 (inverse).

Sequence in context: A374394 A129559 A129680 * A166453 A118233 A255273

Adjacent sequences: A118228 A118229 A118230 * A118232 A118233 A118234

Keyword

sign,tabl

Author

Leroy Quet, Paul D. Hanna, Apr 16 2006

Status

approved