a(n) = Sum_{k=0..n} binomial(n, floor(k/2))*(-2)^(n-k).

Terms

a(0) =1a(1) =-1a(2) =4a(3) =-7a(4) =22a(5) =-46a(6) =130a(7) =-295a(8) =790a(9) =-1870a(10) =4864a(11) =-11782a(12) =30148a(13) =-73984a(14) =187534a(15) =-463687a(16) =1168870a(17) =-2902870a(18) =7293640a(19) =-18161170a(20) =45541492a(21) =-113576596a(22) =284470564a(23) =-710118262a(24) =1777323772a(25) =-4439253196a(26) =11105933440a(27) =-27749232700a(28) =69403169200