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%I #15 Jun 03 2017 19:01:35
%S 1,1,2,4,9,21,51,127,323,834,2179,5743,15238,40637,108800,292200,
%T 786703,2122387,5735596,15522682,42064028,114117541,309918698,
%U 842489130,2292332265,6242655886
%N Number of Motzkin paths of length n with no level steps at height 4.
%H G. C. Greubel, <a href="/A257387/b257387.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = a(n-1) + Sum_{j=0..n-2} A257386(j)*a(n-j).
%F G.f: 1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*R(x)))))))), where R(x) is the g.f. of Riordan numbers (A005043).
%F a(n) ~ 3^(n+1/2)/(24*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Apr 24 2015
%t CoefficientList[Series[1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1+x-Sqrt[1-2*x-3*x^2])/(2*x*(1+x))))))))), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 24 2015 *)
%o (PARI) x='x+O('x^50); Vec(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)))))))))) \\ _G. C. Greubel_, Jun 03 2017
%Y Cf. A005043, A217312, A252354, A257386.
%K nonn
%O 0,3
%A _José Luis Ramírez Ramírez_, Apr 21 2015
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