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

Terms

a(0) =1a(1) =8a(2) =39a(3) =166a(4) =677a(5) =2724a(6) =10915a(7) =43682a(8) =174753a(9) =699040a(10) =2796191a(11) =11184798a(12) =44739229a(13) =178956956a(14) =715827867a(15) =2863311514a(16) =11453246105a(17) =45812984472a(18) =183251937943a(19) =733007751830