a(n) = (F(2*n-1) + F(2*n+1))*(5/6 - cos(2*Pi*n/3)/3), where F(n) = Fibonacci(n).

Terms

a(0) =1a(1) =3a(2) =7a(3) =9a(4) =47a(5) =123a(6) =161a(7) =843a(8) =2207a(9) =2889a(10) =15127a(11) =39603a(12) =51841a(13) =271443a(14) =710647a(15) =930249a(16) =4870847a(17) =12752043a(18) =16692641a(19) =87403803a(20) =228826127a(21) =299537289a(22) =1568397607a(23) =4106118243a(24) =5374978561a(25) =28143753123a(26) =73681302247a(27) =96450076809a(28) =505019158607