a(n) = (5*5^n + (-1)^n)/6.

Terms

a(0) =1a(1) =4a(2) =21a(3) =104a(4) =521a(5) =2604a(6) =13021a(7) =65104a(8) =325521a(9) =1627604a(10) =8138021a(11) =40690104a(12) =203450521a(13) =1017252604a(14) =5086263021a(15) =25431315104a(16) =127156575521a(17) =635782877604