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

1, 2, 4, 8, 14, 30, 50, 112, 182, 420, 672, 1584, 2508, 6006, 9438, 22880, 35750, 87516, 136136, 335920, 520676, 1293292, 1998724, 4992288, 7696444, 19315400, 29716000, 74884320, 115000920, 290845350, 445962870

Offset: 0

Author

Nachum Dershowitz, Aug 30 2020

Keywords

• nonn
• walk

Comments

Also the number of n-step walks on a path graph ending within 3 steps of the origin.

Also the number of monotonic paths of length n ending within 3 steps of the diagonal.

Crossrefs

Cf. A337499, A024483.

Bisections give A162551 (odd part, starting from second element), A051924 (even part).

Formula

a(n) = A337499(n) + (n mod 2)*A024483(floor((n+3)/2)).

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