a(n) = ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n/2.

Terms

a(0) =0a(1) =1a(2) =6a(3) =21a(4) =68a(5) =205a(6) =594a(7) =1673a(8) =4616a(9) =12537a(10) =33630a(11) =89309a(12) =235212a(13) =615173a(14) =1599402a(15) =4137105a(16) =10653712a(17) =27327857a(18) =69856182a(19) =178017061a(20) =452390740a(21) =1146776253a(22) =2900399106a(23) =7320463897a(24) =18441561624a(25) =46376946025a(26) =116442406158a(27) =291929022189a(28) =730881930716