(L(n+2)+2*3^n)/5.

Terms

a(0) =1a(1) =2a(2) =5a(3) =13a(4) =36a(5) =103a(6) =301a(7) =890a(8) =2649a(9) =7913a(10) =23684a(11) =70963a(12) =212745a(13) =638002a(14) =1913629a(15) =5740277a(16) =17219844a(17) =51657935a(18) =154971221a(19) =464909482a(20) =1394721681a(21) =4184154097a(22) =12552444580a(23) =37657305083a(24) =112971868881a(25) =338915531618