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%I #21 Sep 11 2021 13:48:14
%S 1,2,8,44,285,2028,15338,120960,983108,8172094,69116592,592590616,
%T 5136777504,44928712804,395907022448,3510622573064,31296093794827,
%U 280275392413204,2520017580255461,22736733105613548,205767848345966976,1867240544055742660
%N Total number of nodes summed over all lattice paths from (0,0) to (n,n) that do not go below the x-axis or above the diagonal x=y and consist of steps U=(1,1), D=(1,-1) and S=(0,1).
%H Alois P. Heinz, <a href="/A286425/b286425.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ c * d^n / sqrt(n), where d = (3*(71 + 8*sqrt(2))^(1/3))/4 + 51/(4*(71 + 8*sqrt(2))^(1/3)) + 13/4 = 9.443535601593252082001105527294087383986236797... and c = 0.0201623254316291127574085659620180015446126055020315052104102916... - _Vaclav Kotesovec_, Sep 11 2021
%p b:= proc(x, y) option remember; `if`(y<0 or y>x, 0, `if`(x=0, [1$2],
%p (p-> p+[0, p[1]])(b(x, y-1)+b(x-1, y-1)+b(x-1, y+1))))
%p end:
%p a:= n-> b(n$2)[2]:
%p seq(a(n), n=0..30);
%Y Cf. A224769.
%K nonn
%O 0,2
%A _Alois P. Heinz_, May 14 2017
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