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