OFFSET
1,2
COMMENTS
EXAMPLE
Triangle begins:
1;
2, 2;
4, 3, 2;
7, 6, 4, 3;
12, 10, 7, 3, 3;
19, 17, 12, 9, 5, 4;
30, 26, 20, 13, 8, 4, 4;
45, 41, 31, 23, 16, 10, 5, 5;
67, 60, 48, 34, 25, 15, 11, 5, 5;
97, 89, 71, 55, 39, 28, 17, 12, 6, 6;
139, 127, 104, 78, 60, 40, 28, 17, 11, 6, 6;
195, 181, 149, 118, 89, 65, 45, 32, 21, 15, 7, 7;
...
Illustration of initial terms:
Top view
n k of the tower Heights T(n,k)
_
1 1 |_| 1 1
. _ _
2 1 | | 1 1 2
2 2 |_ _| 1 1 2
. _ _ _
3 1 |_| | 2 1 1 4
3 2 | _| 1 1 1 3
3 3 |_ _| 1 1 2
. _ _ _ _
4 1 |_| | | 3 2 1 1 7
4 2 |_ _| | 2 2 1 1 6
4 3 | _| 1 1 1 1 4
4 4 |_ _ _| 1 1 1 3
. _ _ _ _ _
5 1 |_| | | | 5 3 2 1 1 12
5 2 |_ _|_| | 3 3 2 1 1 10
5 3 |_ _| _ _| 2 2 1 1 1 7
5 4 | | 1 1 1 3
5 5 |_ _ _| 1 1 1 3
. _ _ _ _ _ _
6 1 |_| | | | | 7 5 3 2 1 1 19
6 2 |_ _|_| | | 5 5 3 2 1 1 17
6 3 |_ _| _| | 3 3 2 2 1 1 12
6 4 |_ _ _| _| 2 2 2 1 1 1 9
6 5 | _| 1 1 1 1 1 5
6 6 |_ _ _ _| 1 1 1 1 4
.
The levels of the terraces of the tower are the partition numbers A000041 starting from the base.
Note that the top view of the tower is essentially the same as the top view of the stepped pyramid described in A245092 except that in the tower both the symmetric representation of sigma(n) and the symmetric representation of sigma(n-1) are unified in the level 1 of the structure because the first two partitions numbers A000041 are [1, 1].
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Feb 06 2021
STATUS
approved