a(n) = Sum_{k >= 0} 2^k * binomial(k+2,n-2*k).

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =10a(5) =18a(6) =32a(7) =56a(8) =100a(9) =176a(10) =312a(11) =552a(12) =976a(13) =1728a(14) =3056a(15) =5408a(16) =9568a(17) =16928a(18) =29952a(19) =52992a(20) =93760a(21) =165888a(22) =293504a(23) =519296a(24) =918784a(25) =1625600a(26) =2876160a(27) =5088768a(28) =9003520a(29) =15929856