A050195 a(n)=a(n-1)+a(n-2)-d, where d=a(n/5) if 5 divides n, else d=0; 2 initial terms.

1, 1, 2, 3, 4, 7, 11, 18, 29, 46, 75, 121, 196, 317, 511, 828, 1339, 2167, 3506, 5670, 9176, 14846, 24022, 38868, 62886, 101754, 164640, 266394, 431034, 697421, 1128455, 1825876, 2954331, 4780207, 7734527, 12514734, 20249261