a(n) = (Lucas(2*n) - Lucas(n))/2.

Terms

a(0) =0a(1) =1a(2) =2a(3) =7a(4) =20a(5) =56a(6) =152a(7) =407a(8) =1080a(9) =2851a(10) =7502a(11) =19702a(12) =51680a(13) =135461a(14) =354902a(15) =929567a(16) =2434320a(17) =6374236a(18) =16689752a(19) =43697227a(20) =114405500a(21) =299525051a(22) =784179002a(23) =2053027082a(24) =5374926720a(25) =14071792681