a(n) = F(n+3) * F(n+1) + (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.

Terms

a(0) =2a(1) =11a(2) =23a(3) =66a(4) =167a(5) =443a(6) =1154a(7) =3027a(8) =7919a(9) =20738a(10) =54287a(11) =142131a(12) =372098a(13) =974171a(14) =2550407a(15) =6677058a(16) =17480759a(17) =45765227a(18) =119814914a(19) =313679523a(20) =821223647a(21) =2149991426a(22) =5628750623a(23) =14736260451a(24) =38580030722a(25) =101003831723a(26) =264431464439a(27) =692290561602