a(n) = Sum_{k=0..n} C(n-k,4*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =6a(7) =16a(8) =36a(9) =71a(10) =128a(11) =220a(12) =376a(13) =661a(14) =1211a(15) =2290a(16) =4382a(17) =8347a(18) =15706a(19) =29191a(20) =53824a(21) =99009a(22) =182497a(23) =337745a(24) =627401a(25) =1167937a(26) =2174834a(27) =4046070a(28) =7517368a(29) =13951852