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

Author

Omar E. Pol, Jan 23 2014

Keywords

• nonn
• tabf

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).

Examples

			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.