A023561 Convolution of A023531 and (F(2), F(3), F(4), ...).

0, 1, 2, 3, 6, 10, 16, 26, 43, 70, 113, 183, 296, 480, 777, 1257, 2034, 3291, 5325, 8617, 13943, 22560, 36503, 59063, 95566, 154629, 250196, 404826, 655022, 1059848, 1714870, 2774718, 4489588, 7264306