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A235794
Triangle read by rows: T(n,k), n>=1, k>=1, in which column k starts with k zeros and then lists the odd numbers interleaved with k zeros, and the first element of column k is in row k(k+1)/2.
10
0, 1, 0, 0, 3, 0, 0, 1, 5, 0, 0, 0, 0, 0, 7, 3, 0, 0, 0, 1, 9, 0, 0, 0, 0, 5, 0, 0, 11, 0, 0, 0, 0, 0, 3, 0, 13, 7, 0, 1, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 9, 5, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 3, 0, 19, 11, 0, 0, 1, 0, 0, 7, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0
OFFSET
1,5
COMMENTS
It appears that the alternating row sums give A120444, the first differences of A004125, i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = A120444(n).
Row n has length A003056(n) hence the first element of column k is in row A000217(k).
EXAMPLE
Triangle begins:
0;
1;
0, 0;
3, 0;
0, 1;
5, 0, 0;
0, 0, 0;
7, 3, 0;
0, 0, 1;
9, 0, 0, 0;
0, 5, 0, 0;
11, 0, 0, 0;
0, 0, 3, 0;
13, 7, 0, 1;
0, 0, 0, 0, 0;
15, 0, 0, 0, 0;
0, 9, 5, 0, 0;
17, 0, 0, 0, 0;
0, 0, 0, 3, 0;
19, 11, 0, 0, 1;
0, 0, 7, 0, 0, 0;
21, 0, 0, 0, 0, 0;
0, 13, 0, 0, 0, 0;
23, 0, 0, 5, 0, 0;
...
For n = 14 the 14th row of triangle is 13, 7, 0, 1, and the alternating sum is 13 - 7 + 0 - 1 = 5, the same as A120444(14) = 5.
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Jan 23 2014
STATUS
approved