a(n) = -a(n-1) + a(n-2) - F(-n) + 1, a(0) = 1, a(1) = -1, where F() = Fibonacci numbers A000045.

Terms

a(0) =1a(1) =-1a(2) =4a(3) =-6a(4) =14a(5) =-24a(6) =47a(7) =-83a(8) =152a(9) =-268a(10) =476a(11) =-832a(12) =1453a(13) =-2517a(14) =4348a(15) =-7474a(16) =12810a(17) =-21880a(18) =37275a(19) =-63335a(20) =107376a(21) =-181656a(22) =306744a(23) =-517056a(24) =870169a(25) =-1462249a(26) =2453812a(27) =-4112478a(28) =6884102a(29) =-11510808