a(n) = Sum_{k=0..floor(n/8)} binomial(n-4*k,4*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =1a(7) =1a(8) =2a(9) =6a(10) =16a(11) =36a(12) =71a(13) =127a(14) =211a(15) =331a(16) =497a(17) =725a(18) =1047a(19) =1531a(20) =2316a(21) =3668a(22) =6064a(23) =10312a(24) =17717a(25) =30309a(26) =51165a(27) =84893a(28) =138417a(29) =222329