OFFSET
1,6
LINKS
Jinyuan Wang, Table of n, a(n) for n = 1..10000
FORMULA
Triangle read by rows, A054533 * transpose(A101688) (matrix product); i.e., partial sums from of the right of triangle A054533 (because A101688 can be viewed as an upper triangular matrix of 1's).
From Petros Hadjicostas, Jul 28 2019: (Start)
T(n,k) = Sum_{m = k..n} A054533(n,m) = Sum_{d|n} d * mu(n/d) * ((n/d) - ceiling(k/d) + 1) for n >= 1 and 1 <= k <= n.
T(n,k) = phi(n) - Sum_{d|n} d * mu(n/d) * ceiling(k/d) for n >= 2 and 1 <= k <= n.
(End)
EXAMPLE
First few rows of the triangle are as follows:
1;
0, 1;
0, 1, 2;
0, 0, 2, 2;
0, 1, 2, 3, 4;
0, -1, 0, 2, 3, 2;
0, 1, 2, 3, 4, 5, 6;
0, 0, 0, 0, 4, 4, 4, 4;
0, 0, 0, 3, 3, 3, 6, 6, 6;
0, -1, 0, -1, 0, 4, 5, 4, 5, 4;
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
...
row 4 = (0, 0, 2, 2) = partial sums from the right of row 4 of triangle A054533: (0, -2, 0, 2).
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Sep 20 2008
EXTENSIONS
Name edited by and more terms from Petros Hadjicostas, Jul 28 2019
STATUS
approved