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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

Table of n, a(n) for n=0..30.

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 21 16:02 EST 2021. Contains 340352 sequences. (Running on oeis4.)