a(n) = (2*n+1)*Lucas(2*n+1).

Terms

a(0) =1a(1) =12a(2) =55a(3) =203a(4) =684a(5) =2189a(6) =6773a(7) =20460a(8) =60707a(9) =177631a(10) =513996a(11) =1473817a(12) =4194025a(13) =11858508a(14) =33345679a(15) =93320819a(16) =260079468a(17) =722163365a(18) =1998685277a(19) =5515470636a(20) =15180186491a(21) =41680890247a(22) =114197428620a(23) =312260427313a(24) =852296004049