a(n) = Sum_{k>=0} (-1)^k*binomial(n,5*k+3).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =4a(5) =10a(6) =20a(7) =35a(8) =55a(9) =75a(10) =75a(11) =0a(12) =-275a(13) =-1000a(14) =-2625a(15) =-5875a(16) =-11750a(17) =-21250a(18) =-34375a(19) =-47500a(20) =-47500a(21) =0a(22) =171875a(23) =621875a(24) =1628125a(25) =3640625a(26) =7281250a(27) =13171875a(28) =21312500a(29) =29453125