a(n) = (-1)^n * [x^n] Sum_{k>=1} x^(k-1)/(1+3*x^k).

Terms

a(0) =1a(1) =2a(2) =10a(3) =29a(4) =82a(5) =236a(6) =730a(7) =2216a(8) =6571a(9) =19604a(10) =59050a(11) =177410a(12) =531442a(13) =1593596a(14) =4783060a(15) =14351123a(16) =43046722a(17) =129133838a(18) =387420490a(19) =1162281098a(20) =3486785140a(21) =10460294156a(22) =31381059610a(23) =94143358424a(24) =282429536563a(25) =847288078004