Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Sep 11 2021 13:48:53
%S 1,0,3,5,24,78,325,1272,5373,22572,97762,425716,1882062,8375064,
%T 37601643,169773435,771096972,3518065767,16119884297,74125225732,
%U 341970676466,1582133854847,7338641255894,34117910537671,158946919835352,741884929970516,3468677541274922
%N Total number of nodes summed over all lattice paths from (0,0) to (n,0) 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="/A286427/b286427.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ c * 2^n * (1 + sqrt(2))^n / sqrt(n), where c = 0.0205249406642810706349830917137505197586781430984... - _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, 0)[2]:
%p seq(a(n), n=0..30);
%Y Cf. A198324.
%K nonn
%O 0,3
%A _Alois P. Heinz_, May 14 2017