a(n) = Sum_{k=0..n} C(n,floor(k/2))*(-1)^k*3^(n-k).

Terms

a(0) =1a(1) =2a(2) =8a(3) =24a(4) =84a(5) =272a(6) =920a(7) =3040a(8) =10180a(9) =33840a(10) =112968a(11) =376224a(12) =1254696a(13) =4181088a(14) =13939248a(15) =46459584a(16) =154873860a(17) =516229040a(18) =1720795880a(19) =5735921440a(20) =19119861304a(21) =63732624672a(22) =212442552528a(23) =708140901184