%I
%S 0,1,6,28,123,512,2064,8124,31416,119820,451972,1689532,6268276,
%T 23107836,84721796,309151932,1123431812,4067533244,14679173444,
%U 52821023932,189571527236,678748381372,2424976195396,8646702275772
%N Number of even entries in the top rows of all 2compositions of n. 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)=Sum(A181336(n,k), k=0..n).
%C For the case of the odd entries see A181336.
%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. = z(1+zz^2)(1z)^2/[(1+z)(14z+2z^2)^2].
%e a(2)=6 because in (0/2),(1/1),(2/0),(1,0/0,1),(0,1/1,0),(1,1/0,0), and (0,0/1,1) (the 2compositions are written as (top row / bottom row)) we have 1+0+1+1+1+0+2=6 even entries.
%p g := z*(1z)^2*(1+zz^2)/((1+z)*(14*z+2*z^2)^2): gser := series(g, z = 0, 28): seq(coeff(gser, z, n), n = 0 .. 25);
%Y Cf. A181305, A181336.
%K nonn
%O 0,3
%A _Emeric Deutsch_, Oct 14 2010
