a(n) = (F(2n+3) - F(n))/2 where F() = Fibonacci numbers A000045.

Terms

a(0) =1a(1) =2a(2) =6a(3) =16a(4) =43a(5) =114a(6) =301a(7) =792a(8) =2080a(9) =5456a(10) =14301a(11) =37468a(12) =98137a(13) =256998a(14) =672946a(15) =1761984a(16) =4613239a(17) =12078110a(18) =31621701a(19) =82787980a(20) =216743836a(21) =567446112a(22) =1485598681a(23) =3889356696a(24) =10182482353a(25) =26658108074a(26) =69791870526a(27) =182717549872a(28) =478360854115