a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+1,2*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =7a(5) =21a(6) =43a(7) =73a(8) =131a(9) =297a(10) =715a(11) =1593a(12) =3259a(13) =6553a(14) =13723a(15) =29833a(16) =64827a(17) =137881a(18) =289179a(19) =608329a(20) =1293083a(21) =2762457a(22) =5885179a(23) =12478601a(24) =26418363a(25) =56028761a(26) =119072987a(27) =253139017a(28) =537620571a(29) =1140840793