A050192 a(n)=a(n-1)+a(n-2)-d, where d=a(n/2) if n is even, else d=0; 2 initial terms.

1, 0, 1, 1, 2, 2, 4, 5, 9, 12, 21, 31, 52, 79, 131, 205, 336, 532, 868, 1388, 2256, 3623, 5879, 9471, 15350, 24769, 40119, 64809, 104928, 169606, 274534, 443935, 718469, 1162068, 1880537, 3042073, 4922610, 7963815, 12886425