A061926 Square table by antidiagonals where odd rows are partial sums of previous row, even rows are sums of pairs of values in previous row and initial row is 0 and 1 alternating.

0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 2, 2, 1, 0, 1, 2, 3, 3, 1, 0, 0, 3, 4, 6, 4, 1, 0, 1, 3, 5, 10, 9, 5, 1, 0, 0, 4, 6, 15, 16, 14, 6, 1, 0, 1, 4, 7, 21, 25, 30, 19, 7, 1, 0, 0, 5, 8, 28, 36, 55, 44, 26, 8, 1, 0, 1, 5, 9, 36, 49, 91, 85, 70, 33, 9, 1, 0, 0, 6, 10, 45, 64, 140, 146, 155, 96, 42, 10

Offset: 0

Author

Henry Bottomley, May 17 2001

Keywords

• nonn
• tabl

Examples

			From _Sean A. Irvine_, Mar 14 2023: (Start)
Table begins:
  0 1 0  1  0   1   0   1
  0 1 1  2  2   3   3   4
  0 1 2  3  4   5   6   7
  0 1 3  6 10  15  21  28
  0 1 4  9 16  25  36  49
  0 1 5 14 30  55  91 140
  0 1 6 19 44  85 146 231
  0 1 7 26 70 155 301 532
(End)
		

Crossrefs

Rows are A000035, A004526, A001477, A000217, A000290, A000330, A005900, A006325, A014820, A061927. Columns are A000004, A000012, A001477, A061925.

Formula

T(0, 2*k) = 0, T(0, 2*k+1) = 1, T(n, 0) = 0, T(2*n, k) = T(2*n-1, k-1) + T(2*n-1, k), T(2*n+1, k) = T(2*n+1, k-1) + T(2*n, k). - Sean A. Irvine, Mar 14 2023