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A272026 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists the numbers A016945 interleaved with k-1 zeros, and the first element of column k is in row k(k+1)/2. 4
3, 9, 15, 3, 21, 0, 27, 9, 33, 0, 3, 39, 15, 0, 45, 0, 0, 51, 21, 9, 57, 0, 0, 3, 63, 27, 0, 0, 69, 0, 15, 0, 75, 33, 0, 0, 81, 0, 0, 9, 87, 39, 21, 0, 3, 93, 0, 0, 0, 0, 99, 45, 0, 0, 0, 105, 0, 27, 15, 0, 111, 51, 0, 0, 0, 117, 0, 0, 0, 9, 123, 57, 33, 0, 0, 3, 129, 0, 0, 21, 0, 0, 135, 63, 0, 0, 0, 0, 141, 0, 39, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Alternating sum of row n equals 3 times sigma(n), i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = 3*A000203(n) = A272027(n).
Row n has length A003056(n) hence the first element of column k is in row A000217(k).
The number of positive terms in row n is A001227(n).
If T(n,k) = 9 then T(n+1,k+1) = 3 is the first element of the column k+1.
For more information see A196020.
LINKS
FORMULA
T(n,k) = 3*A196020(n,k) = A196020(n,k) + A236106(n,k).
EXAMPLE
Triangle begins:
3;
9;
15, 3;
21, 0;
27, 9;
33, 0, 3;
39, 15, 0;
45, 0, 0;
51, 21, 9;
57, 0, 0, 3;
63, 27, 0, 0;
69, 0, 15, 0;
75, 33, 0, 0;
81, 0, 0, 9;
87, 39, 21, 0, 3;
93, 0, 0, 0, 0;
99, 45, 0, 0, 0;
105, 0, 27, 15, 0;
111, 51, 0, 0, 0;
117, 0, 0, 0, 9;
123, 57, 33, 0, 0, 3;
129, 0, 0, 21, 0, 0;
135, 63, 0, 0, 0, 0;
141, 0, 39, 0, 0, 0;
...
For n = 9 the divisors of 9 are 1, 3, 9, therefore the sum of the divisors of 9 is 1 + 3 + 9 = 13 and 3*13 = 39. On the other hand the 9th row of triangle is 51, 21, 9, therefore the alternating row sum is 51 - 21 + 9 = 39, equaling 3 times sigma(9).
CROSSREFS
Column 1 is A016945.
Sequence in context: A332660 A343144 A050005 * A152247 A253765 A077932
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Apr 18 2016
STATUS
approved

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)