Number of winning length n strings with a 3-symbol alphabet in "same game".

Terms

a(0) =1a(1) =0a(2) =3a(3) =3a(4) =15a(5) =33a(6) =105a(7) =297a(8) =879a(9) =2631a(10) =7833a(11) =23697a(12) =71385a(13) =216765a(14) =657849a(15) =2003151a(16) =6103743a(17) =18624693a(18) =56870385a(19) =173760513a(20) =531128349a(21) =1623881889a(22) =4965695331a(23) =15185222199a(24) =46435889601a(25) =141985777503