a(n) is the number of ballot sequences of length n tied or won by at most 3 votes.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =14a(5) =30a(6) =50a(7) =112a(8) =182a(9) =420a(10) =672a(11) =1584a(12) =2508a(13) =6006a(14) =9438a(15) =22880a(16) =35750a(17) =87516a(18) =136136a(19) =335920a(20) =520676a(21) =1293292a(22) =1998724a(23) =4992288a(24) =7696444a(25) =19315400a(26) =29716000a(27) =74884320a(28) =115000920a(29) =290845350