a(n) = F(n)*F(n+1) + F(n+2), where F = A000045 (Fibonacci numbers).

Terms

a(0) =1a(1) =3a(2) =5a(3) =11a(4) =23a(5) =53a(6) =125a(7) =307a(8) =769a(9) =1959a(10) =5039a(11) =13049a(12) =33929a(13) =88451a(14) =230957a(15) =603667a(16) =1578823a(17) =4130829a(18) =10810469a(19) =28295411a(20) =74067401a(21) =193893263a(22) =507590495a(23) =1328842801a(24) =3478880593a(25) =9107706243a(26) =23844088085a(27) =62424315227a(28) =163428464759a(29) =427860443429