a(n) = L(n)^2 - 5*(-1)^n = L(n+1)*L(n-1), where L = A000032.

Terms

a(0) =-1a(1) =6a(2) =4a(3) =21a(4) =44a(5) =126a(6) =319a(7) =846a(8) =2204a(9) =5781a(10) =15124a(11) =39606a(12) =103679a(13) =271446a(14) =710644a(15) =1860501a(16) =4870844a(17) =12752046a(18) =33385279a(19) =87403806a(20) =228826124a(21) =599074581a(22) =1568397604a(23) =4106118246a(24) =10749957119a(25) =28143753126a(26) =73681302244a(27) =192900153621a(28) =505019158604