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 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}. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A342419 A226350 A112609 * A054015 A056137 A332602 Adjacent sequences:  A134360 A134361 A134362 * A134364 A134365 A134366 KEYWORD sign,tabf AUTHOR Leroy Quet, Oct 22 2007 STATUS approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)