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%I #30 Sep 08 2022 08:44:55
%S 0,0,3,12,55,210,826,3136,12027,45870,175846,674784,2598102,10024196,
%T 38771188,150250496,583368787,2268706134,8836184878,34461323872,
%U 134563944322,526023515996,2058355584748,8061896050432,31602643220830,123979613859660,486734822857596
%N a(n) = (C(2n, n)/2 - (2^(n-1) + ((n+1) mod 2)*C(n-1, n/2-1)))/2.
%C Number of distinct asymmetric staircase walks connecting opposite corners of a square grid of side n > 1. - _Christian Barrientos_, Nov 25 2018
%H Vincenzo Librandi, <a href="/A042971/b042971.txt">Table of n, a(n) for n = 1..1000</a>
%e U = up, R = right Example of asymmetric staircase walk: URURUURR. - _Christian Barrientos_, Nov 29 2018
%t Table[Binomial[2n,n]/2-(2^(n-1)+Mod[n+1,2]Binomial[n-1, n/2-1]),{n,30}]/2
%o (PARI) a(n) = (binomial(2*n,n)/2 - (2^(n-1) + if (((n+1) % 2), binomial( n-1, n/2-1))))/2; \\ _Michel Marcus_, Nov 25 2018
%o (Magma) [(Binomial(2*n,n) -(2^n +(1+(-1)^n)*Binomial(n-1, Floor(n/2)-1) ))/4: n in [1..30]]; // _G. C. Greubel_, Feb 17 2019
%o (Sage) [(binomial(2*n,n) -(2^n + (1+(-1)^n)*binomial(n-1, floor(n/2)-1)))/4 for n in (1..30)] # _G. C. Greubel_, Feb 17 2019
%Y Cf. A027306 (for symmetric staircase walks).
%K nonn
%O 1,3
%A _Wouter Meeussen_