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A365434
Irregular triangle read by rows: T(n,k) is the number of cubes in the k-th level of the ziggurat of order n described in A347186, n >= 1, k >= 1.
2
1, 3, 1, 4, 2, 7, 5, 3, 1, 6, 4, 2, 12, 9, 7, 5, 3, 1, 8, 6, 4, 2, 15, 13, 11, 9, 7, 5, 3, 1, 13, 9, 7, 5, 2, 18, 16, 14, 12, 10, 8, 6, 4, 2, 12, 10, 8, 6, 4, 2, 28, 24, 22, 20, 16, 14, 12, 9, 7, 5, 3, 1, 14, 12, 10, 8, 6, 4, 2, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 24, 19, 17, 15, 11, 9, 7, 3, 1, 1
OFFSET
1,2
COMMENTS
The values of n when the number of terms in row n is equal to n give A174973.
The values of n when the number of terms in row n is not equal to n give A238524.
If and only if n is a power of 2 then row n lists the first n odd numbers in decreasing order.
If and only if n is an odd prime then row n lists the first (n + 1)/2 positive even numbers in decreasing order.
If and only if n is an even perfect number then row n lists 2*n together with the first n - 1 odd numbers in decreasing order.
EXAMPLE
Triangle begins:
1;
3, 1;
4, 2;
7, 5, 3, 1;
6, 4, 2;
12, 9, 7, 5, 3, 1;
8, 6, 4, 2;
15, 13, 11, 9, 7, 5, 3, 1;
13, 9, 7, 5, 2;
18, 16, 14, 12, 10, 8, 6, 4, 2;
12, 10, 8, 6, 4, 2;
28, 24, 22, 20, 16, 14, 12, 9, 7, 5, 3, 1;
14, 12, 10, 8, 6, 4, 2;
24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2;
24, 19, 17, 15, 11, 9, 7, 3, 1, 1;
31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1;
...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Oct 19 2023
STATUS
approved