a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k+1,2*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =7a(4) =21a(5) =43a(6) =93a(7) =251a(8) =661a(9) =1587a(10) =3805a(11) =9499a(12) =23813a(13) =58691a(14) =144141a(15) =356491a(16) =883637a(17) =2184115a(18) =5391869a(19) =13325371a(20) =32953317a(21) =81459235a(22) =201299565a(23) =497518187a(24) =1229819541a(25) =3039854611a(26) =7513347421a(27) =18570354203a(28) =45900859333a(29) =113454099843