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%I #24 Aug 24 2020 00:57:45
%S 4,12,60,364,2448,17556,131560,1017900,8069424,65204656,535070172,
%T 4446927732,37353738800,316621743480,2704784196240,23263187479980,
%U 201275443944432,1750651680235920,15298438066553776,134252511729576240,1182622941581590080
%N a(n) = 3*binomial(4*n,n)/(4*n-1).
%C a(n) is the number of lattice paths from (0,0) to (3n,n) using only the steps (1,0) and (0,1) and whose only lattice points on the line y = x/3 are the path's endpoints. - _Lucas A. Brown_, Aug 21 2020
%F a(n) = 4*A006632(n).
%F G.f.: 4*x*F(x)^3 where F(x) = 1 + x*F(x)^4 is the g.f. of A002293.
%t Array[3 Binomial[4 #, #]/(4 # - 1) &, 21] (* _Michael De Vlieger_, Aug 21 2020 *)
%o (PARI) a(n) = {3*binomial(4*n,n)/(4*n-1)} \\ _Andrew Howroyd_, Aug 21 2020
%Y Cf. A006632, A337292.
%K nonn,easy
%O 1,1
%A _Lucas A. Brown_, Aug 21 2020