a(n) = floor(Lucas(n+1)/2), Lucas(n) = A000032(n).

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =5a(5) =9a(6) =14a(7) =23a(8) =38a(9) =61a(10) =99a(11) =161a(12) =260a(13) =421a(14) =682a(15) =1103a(16) =1785a(17) =2889a(18) =4674a(19) =7563a(20) =12238a(21) =19801a(22) =32039a(23) =51841a(24) =83880a(25) =135721a(26) =219602a(27) =355323a(28) =574925a(29) =930249