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

Terms

a(0) =1a(1) =2a(2) =5a(3) =8a(4) =15a(5) =24a(6) =41a(7) =66a(8) =109a(9) =176a(10) =287a(11) =464a(12) =753a(13) =1218a(14) =1973a(15) =3192a(16) =5167a(17) =8360a(18) =13529a(19) =21890a(20) =35421a(21) =57312a(22) =92735a(23) =150048a(24) =242785a(25) =392834a(26) =635621a(27) =1028456a(28) =1664079a(29) =2692536