a(n) = (2*5^n + 3*(-1)^(floor((n-1)/3)) + (-1)^n)/6.

Terms

a(0) =0a(1) =2a(2) =9a(3) =42a(4) =208a(5) =1041a(6) =5208a(7) =26042a(8) =130209a(9) =651042a(10) =3255208a(11) =16276041a(12) =81380208a(13) =406901042a(14) =2034505209a(15) =10172526042a(16) =50862630208a(17) =254313151041