OFFSET
1,2
COMMENTS
Left border = A000203, sigma(n): (1, 3, 4, 7, 6, ...). Row sums = A007429: (1, 4, 5, 11, 7, 20, 9, ...); = inverse Moebius transform applied to sigma(n); (i.e., inverse Moebius transform applied twice to natural numbers).
T(n,k) is the total number of parts congruent to 0 mod k in the partitions of n into equal parts. - Omar E. Pol, Nov 19 2019
From Omar E. Pol, Jan 01 2020: (Start)
Conjecture 1: the sum of odd-indexed terms in row n equals A327096(n).
Conjecture 2: the sum of even-indexed terms in row n equals the n-th term of the sequence formed by A000004 and A007429 interleaved.
Conjecture 3: alternating row sums give A288417. (End)
EXAMPLE
First few rows of the triangle are:
1;
3, 1;
4, 0, 1;
7, 3, 0, 1;
6, 0, 0, 0, 1;
12, 4, 3, 0, 0, 1;
8, 0, 0, 0, 0, 0, 1;
15, 7, 0, 3, 0, 0, 0, 1;
13, 0, 4, 0, 0, 0, 0, 0, 1;
18, 6, 0, 0, 3, 0, 0, 0, 0, 1;
12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
28, 12, 7, 4, 0, 3, 0, 0, 0, 0, 0, 1;
14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
24, 8, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1;
24, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
31, 15, 0, 7, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1;
...
Extended by Omar E. Pol, Nov 19 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 03 2007
EXTENSIONS
New name and more terms from Omar E. Pol, Nov 19 2019
STATUS
approved