a(n) = F(n)^2 + 4*(-1)^n = F(n+3)*F(n-3), where F = A000045.

Terms

a(0) =4a(1) =-3a(2) =5a(3) =0a(4) =13a(5) =21a(6) =68a(7) =165a(8) =445a(9) =1152a(10) =3029a(11) =7917a(12) =20740a(13) =54285a(14) =142133a(15) =372096a(16) =974173a(17) =2550405a(18) =6677060a(19) =17480757a(20) =45765229a(21) =119814912a(22) =313679525a(23) =821223645a(24) =2149991428a(25) =5628750621a(26) =14736260453a(27) =38580030720a(28) =101003831725a(29) =264431464437