a(n) = -1/6 + (-1)^n/2 + 2*4^n/3.

Terms

a(0) =1a(1) =2a(2) =11a(3) =42a(4) =171a(5) =682a(6) =2731a(7) =10922a(8) =43691a(9) =174762a(10) =699051a(11) =2796202a(12) =11184811a(13) =44739242a(14) =178956971a(15) =715827882a(16) =2863311531a(17) =11453246122a(18) =45812984491a(19) =183251937962a(20) =733007751851