a(n) = Sum_{k=0..n} (-1)^k*F(k)*F(k+3), where F=A000045 (Fibonacci numbers).

Terms

a(0) =0a(1) =-3a(2) =2a(3) =-14a(4) =25a(5) =-80a(6) =192a(7) =-523a(8) =1346a(9) =-3550a(10) =9265a(11) =-24288a(12) =63552a(13) =-166419a(14) =435650a(15) =-1140590a(16) =2986057a(17) =-7817648a(18) =20466816a(19) =-53582875a(20) =140281730a(21) =-367262398a(22) =961505377a(23) =-2517253824a(24) =6590256000a(25) =-17253514275a(26) =45170286722a(27) =-118257345998