%I
%S 2,6,22,78,272,940,3232,11080,37920,129648,443008,1513248,5168000,
%T 17647552,60258304,205746304,702484992,2398480128,8189016064,
%U 27959235072,95459170304,325918735360,1112757649408,3799195224064
%N Number of 2compositions of n containing at least one 0 entry. A 2composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
%C a(n)=A181365(n,0).
%D G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of Lconvex polyominoes, European Journal of Combinatorics, 28, 2007, 17241741.
%F G.f.=2z(1z)^3/[(12z)(14z+2z^2)].
%e a(2)=6 because the 2compositions of 2, written as (top row / bottom row), are (1/1), (0/2), (2/0), (1,0/0,1), (0,1/1,0), (1,1/0,0), (0,0/1,1) and only the first one does not contain a 0 entry.
%p G := 2*z*(1z)^3/((12*z)*(14*z+2*z^2)): Gser := series(G, z = 0, 30): seq(coeff(Gser, z, n), n = 1 .. 25);
%t CoefficientList[Series[(2x (1x)^3)/((12x)(14x+2x^2)),{x,0,30}],x] (* _Harvey P. Dale_, Mar 29 2020 *)
%Y Cf. A181365
%K nonn
%O 1,1
%A _Emeric Deutsch_, Oct 15 2010
