a(n) = Sum_{k=0..floor(n/8)} (-1)^k * 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) =0a(9) =-4a(10) =-14a(11) =-34a(12) =-69a(13) =-125a(14) =-209a(15) =-329a(16) =-493a(17) =-705a(18) =-955a(19) =-1199a(20) =-1324a(21) =-1092a(22) =-56a(23) =2560a(24) =8025a(25) =18313a(26) =36353a(27) =66273a(28) =113525a(29) =184653