A127710 Inverse of the triangle A(n,k)=if(k<=n,if(n<=2k,1/(n+1),0),0).

1, 0, 2, 0, -2, 3, 0, 2, -3, 4, 0, 0, 0, -4, 5, 0, -2, 3, 0, -5, 6, 0, 0, 0, 0, 0, -6, 7, 0, 2, -3, 4, 0, 0, -7, 8, 0, 0, 0, 0, 0, 0, 0, -8, 9, 0, 0, 0, -4, 5, 0, 0, 0, -9, 10, 0, 0

Offset

0,3

Comments

It is conjectured that all elements of this triangle are integers. It appears that the row sums are the ruler function A001511.

Links

Table of n, a(n) for n=0..56.

Example

Triangle begins
1,
0, 2,
0, -2, 3,
0, 2, -3, 4,
0, 0, 0, -4, 5,
0, -2, 3, 0, -5, 6,
0, 0, 0, 0, 0, -6, 7,
0, 2, -3, 4, 0, 0, -7, 8,
0, 0, 0, 0, 0, 0, 0, -8, 9,
0, 0, 0, -4, 5, 0, 0, 0, -9, 10,
0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 11,
0, -2, 3, 0, -5, 6, 0, 0, 0, 0, -11, 12,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 13
Triangle is the inverse of the triangle
1,
0, 1/2,
0, 1/3, 1/3,
0, 0, 1/4, 1/4,
0, 0, 1/5, 1/5, 1/5,
0, 0, 0, 1/6, 1/6, 1/6,
0, 0, 0, 1/7, 1/7, 1/7, 1/7,
0, 0, 0, 0, 1/8, 1/8, 1/8, 1/8,
0, 0, 0, 0, 1/9, 1/9, 1/9, 1/9, 1/9,
0, 0, 0, 0, 0, 1/10, 1/10, 1/10, 1/10, 1/10,
0, 0, 0, 0, 0, 1/11, 1/11, 1/11, 1/11, 1/11, 1/11

Crossrefs

Sequence in context: A111565 A299761 A141099 * A137510 A247303 A067871

Adjacent sequences: A127707 A127708 A127709 * A127711 A127712 A127713

Keyword

sign,tabl

Author

Paul Barry, Jan 24 2007

Status

approved