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A337500 a(n) is the number of ballot sequences of length n tied or won by at most 3 votes. 0

%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 n-step 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 D-finite with recurrence -(n+3)*(n-4)*a(n) +2*(n^2-2*n-11)*a(n-1) +4*(n-1)^2*a(n-2) -8*(n-1)*(n-2)*a(n-3)=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

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Last modified March 8 10:56 EST 2021. Contains 341948 sequences. (Running on oeis4.)