a(n) = (5^n + 5^floor(n/2))/2.

Terms

a(0) =1a(1) =3a(2) =15a(3) =65a(4) =325a(5) =1575a(6) =7875a(7) =39125a(8) =195625a(9) =976875a(10) =4884375a(11) =24415625a(12) =122078125a(13) =610359375a(14) =3051796875a(15) =15258828125a(16) =76294140625a(17) =381469921875