a(n) = Sum_{k=0..floor(n/5)} C(n-3*k,2*k) * 2^k.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =3a(6) =7a(7) =13a(8) =21a(9) =31a(10) =47a(11) =77a(12) =133a(13) =231a(14) =391a(15) =645a(16) =1053a(17) =1727a(18) =2863a(19) =4781a(20) =7989a(21) =13303a(22) =22071a(23) =36565a(24) =60621a(25) =100655a(26) =167295a(27) =278077a(28) =461989a(29) =767143