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

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =15a(5) =54a(6) =216a(7) =810a(8) =3105a(9) =11745a(10) =44631a(11) =169128a(12) =641520a(13) =2431944a(14) =9221121a(15) =34959195a(16) =132543135a(17) =502506990a(18) =1905156936a(19) =7222991778a(20) =27384465825a(21) =103822372809a(22) =393620574951