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

Terms

a(0) =1a(1) =1a(2) =1a(3) =5a(4) =13a(5) =33a(6) =73a(7) =157a(8) =325a(9) =665a(10) =1345a(11) =2709a(12) =5437a(13) =10897a(14) =21817a(15) =43661a(16) =87349a(17) =174729a(18) =349489a(19) =699013a(20) =1398061a(21) =2796161a(22) =5592361a(23) =11184765a(24) =22369573a(25) =44739193a(26) =89478433a(27) =178956917a(28) =357913885a(29) =715827825