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A340525 Triangle read by rows: T(n,k) = A006218(n-k+1)*A002865(k-1), 1 <= k <= n. 3
1, 3, 0, 5, 0, 1, 8, 0, 3, 1, 10, 0, 5, 3, 2, 14, 0, 8, 5, 6, 2, 16, 0, 10, 8, 10, 6, 4, 20, 0, 14, 10, 16, 10, 12, 4, 23, 0, 16, 14, 20, 16, 20, 12, 7, 27, 0, 20, 16, 28, 20, 32, 20, 21, 8, 29, 0, 23, 20, 32, 28, 40, 32, 35, 24, 12, 35, 0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Conjecture: the sum of row n equals A006128(n), the total number of parts in all partitions of n.
LINKS
EXAMPLE
Triangle begins:
1;
3, 0;
5, 0, 1;
8, 0, 3, 1;
10, 0, 5, 3, 2;
14, 0, 8, 5, 6, 2;
16, 0, 10, 8, 10, 6, 4;
20, 0, 14, 10, 16, 10, 12, 4;
23, 0, 16, 14, 20, 16, 20, 12, 7;
27, 0, 20, 16, 28, 20, 32, 20, 21, 8;
29, 0, 23, 20, 32, 28, 40, 32, 35, 24, 12;
35, 0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14;
...
For n = 6 the calculation of every term of row 6 is as follows:
--------------------------
k A002865 T(6,k)
--------------------------
1 1 * 14 = 14
2 0 * 10 = 0
3 1 * 8 = 8
4 1 * 5 = 5
5 2 * 3 = 6
6 2 * 1 = 2
--------------------------
The sum of row 6 is 14 + 0 + 8 + 5 + 6 + 2 = 35, equaling A006128(6).
CROSSREFS
Mirror of A245095.
Row sums give A006128 (conjectured).
Columns 1, 3 and 4 are A006218.
Column 2 gives A000004.
Leading diagonal gives A002865.
Sequence in context: A276833 A166586 A122274 * A003966 A123931 A058026
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Jan 10 2021
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)