A096966 Triangle (read by rows) in which the number of entries in a row only increases by 1 every other row, the first column and the 'diagonal' is set to all 1's and a(i,j) = a(i-1,j) + a(i-1,j-1) + a(i-2,j-1) + a(i-3,j-1) for other entries.

1, 1, 1, 1, 1, 4, 1, 7, 1, 1, 10, 13, 1, 13, 34, 1, 1, 16, 64, 49, 1, 19, 103, 160, 1, 1, 22, 151, 361, 211, 1, 25, 208, 679, 781, 1, 1, 28, 274, 1141, 1981, 994, 1, 31, 349, 1774, 4162, 3967, 1, 1, 34, 433, 2605, 7756, 10891, 4963, 1, 37, 526, 3661, 13276, 24790, 20815, 1