Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = sqrt(2).

Terms

a(0) =1a(1) =3a(2) =5a(3) =9a(4) =18a(5) =35a(6) =66a(7) =124a(8) =234a(9) =441a(10) =829a(11) =1557a(12) =2925a(13) =5496a(14) =10325a(15) =19394a(16) =36429a(17) =68428a(18) =128532a(19) =241425a(20) =453475a(21) =851775a(22) =1599910a(23) =3005145a(24) =5644626a(25) =10602419a(26) =19914742a(27) =37406262a(28) =70260933a(29) =131972522