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

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =17a(5) =44a(6) =124a(7) =352a(8) =977a(9) =2654a(10) =7128a(11) =19088a(12) =51185a(13) =137560a(14) =370248a(15) =997088a(16) =2685105a(17) =7229274a(18) =19460284a(19) =52380120a(20) =140986721a(21) =379487812a(22) =1021471780a(23) =2749540160a(24) =7401082337a(25) =19921861942a(26) =53624552944a(27) =144343351328a(28) =388534532129