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

Terms

a(0) =1a(1) =4a(2) =10a(3) =13a(4) =68a(5) =178a(6) =233a(7) =1220a(8) =3194a(9) =4181a(10) =21892a(11) =57314a(12) =75025a(13) =392836a(14) =1028458a(15) =1346269a(16) =7049156a(17) =18454930a(18) =24157817a(19) =126491972a(20) =331160282a(21) =433494437a(22) =2269806340a(23) =5942430146a(24) =7778742049a(25) =40730022148a(26) =106632582346