OFFSET
1,1
COMMENTS
FORMULA
T(n,k) = 2*A196020(n,k).
EXAMPLE
Triangle begins:
2;
6;
10, 2;
14, 0;
18, 6;
22, 0, 2;
26, 10, 0;
30, 0, 0;
34, 14, 6;
38, 0, 0, 2;
42, 18, 0, 0;
46, 0, 10, 0;
50, 22, 0, 0;
54, 0, 0, 6;
58, 26, 14, 0, 2;
62, 0, 0, 0, 0;
66, 30, 0, 0, 0;
70, 0, 18, 10, 0;
74, 34, 0, 0, 0;
78, 0, 0, 0, 6;
82, 38, 22, 0, 0, 2;
86, 0, 0, 14, 0, 0;
90, 42, 0, 0, 0, 0;
94, 0, 26, 0, 0, 0;
...
For n = 9 the divisors of 2*9 = 18 are 1, 2, 3, 6, 9, 18, therefore the sum of the even divisors of 18 is 2 + 6 + 18 = 26. On the other hand the 9th row of triangle is 34, 14, 6, therefore the alternating row sum is 34 - 14 + 6 = 26, equaling the sum of the even divisors of 18.
If n is even then the alternating sum of the n-th row of triangle is simpler than the sum of the even divisors of 2n. Example: for n = 12 the sum of the even divisors of 2*12 = 24 is 2 + 4 + 6 + 8 + 12 + 24 = 56, and the alternating sum of the 12th row of triangle is 46 - 0 + 10 - 0 = 56.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Jan 23 2014
STATUS
approved