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

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =13a(5) =25a(6) =49a(7) =91a(8) =169a(9) =306a(10) =551a(11) =979a(12) =1729a(13) =3029a(14) =5279a(15) =9150a(16) =15793a(17) =27149a(18) =46513a(19) =79439a(20) =135301a(21) =229866a(22) =389643a(23) =659111a(24) =1112833a(25) =1875625a(26) =3156219a(27) =5303286a(28) =8898709a(29) =14912641