A050194 a(n)=a(n-1)+a(n-2)-d, where d=a(n/4) if 4 divides n, else d=0; 2 initial terms.

1, 1, 2, 2, 4, 6, 10, 15, 25, 40, 65, 103, 168, 271, 439, 708, 1147, 1855, 3002, 4853, 7855, 12708, 20563, 33265, 53828, 87093, 140921, 228004, 368925, 596929, 965854, 1562768, 2528622, 4091390, 6620012, 10711377, 17331389