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

Terms

a(0) =1a(1) =3a(2) =11a(3) =45a(4) =189a(5) =799a(6) =3383a(7) =14329a(8) =60697a(9) =257115a(10) =1089155a(11) =4613733a(12) =19544085a(13) =82790071a(14) =350704367a(15) =1485607537a(16) =6293134513a(17) =26658145587a(18) =112925716859a(19) =478361013021