This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337500 #9 Oct 29 2021 07:39:03 %S A337500 1,2,4,8,14,30,50,112,182,420,672,1584,2508,6006,9438,22880,35750, %T A337500 87516,136136,335920,520676,1293292,1998724,4992288,7696444,19315400, %U A337500 29716000,74884320,115000920,290845350,445962870 %N A337500 a(n) is the number of ballot sequences of length n tied or won by at most 3 votes. %C A337500 Also the number of n-step walks on a path graph ending within 3 steps of the origin. %C A337500 Also the number of monotonic paths of length n ending within 3 steps of the diagonal. %F A337500 a(n) = A337499(n) + (n mod 2)*A024483(floor((n+3)/2)). %F A337500 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 A337500 Cf. A337499, A024483. %Y A337500 Bisections give A162551 (odd part, starting from second element), A051924 (even part). %K A337500 nonn,walk %O A337500 0,2 %A A337500 _Nachum Dershowitz_, Aug 30 2020