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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
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. LINKS 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 CROSSREFS Cf. A337499, A024483. Bisections give A162551 (odd part, starting from second element), A051924 (even part). Sequence in context: A118560 A187813 A038024 * A061297 A130711 A093483 Adjacent sequences:  A337497 A337498 A337499 * A337501 A337502 A337503 KEYWORD nonn,walk AUTHOR Nachum Dershowitz, Aug 30 2020 STATUS approved

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Last modified January 24 00:05 EST 2022. Contains 350515 sequences. (Running on oeis4.)