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.

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).

Links

Table of n, a(n) for n=1..83.

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.

Crossrefs

Cf. A000203, A000217, A003056, A004125, A120444, A196020, A211343, A228813, A231345, A231347, A235791, A236104, A236106, A236112.

Sequence in context: A126723 A325846 A325735 * A349911 A090030 A293616

Adjacent sequences: A235791 A235792 A235793 * A235795 A235796 A235797

Keyword

nonn,tabf

Author

Omar E. Pol, Jan 23 2014

Status

approved