|
|
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
|
|
|
KEYWORD
|
sign,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|