%I
%S 1,2,4,8,14,30,50,112,182,420,672,1584,2508,6006,9438,22880,35750,
%T 87516,136136,335920,520676,1293292,1998724,4992288,7696444,19315400,
%U 29716000,74884320,115000920,290845350,445962870
%N a(n) is the number of ballot sequences of length n tied or won by at most 3 votes.
%C Also the number of nstep walks on a path graph ending within 3 steps of the origin.
%C Also the number of monotonic paths of length n ending within 3 steps of the diagonal.
%F a(n) = A337499(n) + (n mod 2)*A024483(floor((n+3)/2)).
%F Conjecture Dfinite with recurrence (n+3)*(n4)*a(n) +2*(n^22*n11)*a(n1) +4*(n1)^2*a(n2) 8*(n1)*(n2)*a(n3)=0.  _R. J. Mathar_, Sep 27 2020
%Y Cf. A337499, A024483.
%Y Bisections give A162551 (odd part, starting from second element), A051924 (even part).
%K nonn,walk
%O 0,2
%A _Nachum Dershowitz_, Aug 30 2020
