A134363 Irregular triangle read by rows where n-th row (of A061395(n) terms, for n>=2) is such that n = Product_{j=1..A061395(n)} prime(j)^(Sum_{k=1..j} T(n,k)). Row 1 is {0}.

0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 3, 0, 2, 1, -1, 1, 0, 0, 0, 0, 1, 2, -1, 0, 0, 0, 0, 0, 1, 1, -1, 0, 1, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, -2, 1, 0, 1, -1, 1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, -2, 0, 0, 2

Offset

1,5

Comments

The rows of this triangle also give all the ordered ways that a finite number of integers can be arranged so that their partial sums, from left to right, are all nonnegative and their total sum is positive.

Links

Table of n, a(n) for n=1..84.

Example

Triangle begins:
  0;
  1;
  0, 1;
  2;
  0, 0, 1;
  1, 0;
  0, 0, 0, 1;
  3;
  ...
Row 20 is {2, -2, 1}. So 20 = prime(1)^T(20,1) * prime(2)^(T(20,1) + T(20,2)) * prime(3)^(T(20,1) + T(20,2) + T(20,3)) = 2^2 * 3^(2 - 2) * 5^(2 - 2 + 1) = 2^2 * 3^0 * 5^1.

Crossrefs

Cf. A061395, A067255, A134364.

Sequence in context: A226350 A373898 A112609 * A054015 A373976 A369164

Adjacent sequences: A134360 A134361 A134362 * A134364 A134365 A134366

Keyword

sign,tabf

Author

Leroy Quet, Oct 22 2007

Status

approved