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%I #8 Apr 29 2015 06:35:12
%S 1,0,1,0,2,1,5,4,15,15,48,57,162,218,570,842,2070,3284,7709,12922,
%T 29299,51255,113220,204781,443574,823554,1757947,3331818,7035054,
%U 13552699,28387680,55401396,115369417,227501256,471780468,938107057,1939727280,3883120002
%N Number of 3-generalized Motzkin paths of length n with no level steps H=(3,0) at even level.
%F G.f.: (1-x^3-sqrt((1-x^3)*(1-4*x^2-x^3)))/(2*x^2).
%e For n=6 we have 5 paths: UDUDUD, UUDDUD, UDUUDD, UUUDDD and UUDUDD
%t CoefficientList[Series[(1-x^3-Sqrt[(1-x^3)*(1-4*x^2-x^3)])/(2*x^2), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 27 2015 *)
%Y Cf. A002212, A090345.
%K nonn
%O 0,5
%A _José Luis Ramírez Ramírez_, Apr 27 2015