Number of winning length n strings with a 2-symbol alphabet in "same game".

Terms

a(0) =1a(1) =0a(2) =2a(3) =2a(4) =6a(5) =12a(6) =26a(7) =58a(8) =126a(9) =278a(10) =602a(11) =1300a(12) =2774a(13) =5878a(14) =12350a(15) =25778a(16) =53470a(17) =110332a(18) =226610a(19) =463602a(20) =945214a(21) =1921550a(22) =3896642a(23) =7885092a(24) =15927086a(25) =32121582a(26) =64697726a(27) =130166378a(28) =261637446a(29) =525478668