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A181337 Number of even entries in the top rows of all 2-compositions of n. A 2-composition 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.

%I A181337 #4 Jul 24 2022 13:58:12
%S A181337 0,1,6,28,123,512,2064,8124,31416,119820,451972,1689532,6268276,
%T A181337 23107836,84721796,309151932,1123431812,4067533244,14679173444,
%U A181337 52821023932,189571527236,678748381372,2424976195396,8646702275772
%N A181337 Number of even entries in the top rows of all 2-compositions of n. A 2-composition 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 A181337 a(n)=Sum(A181336(n,k), k=0..n).
%C A181337 For the case of the odd entries see A181336.
%D A181337 G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European Journal of Combinatorics, 28, 2007, 1724-1741.
%H A181337 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12,-4,12,-4).
%F A181337 G.f. = z(1+z-z^2)(1-z)^2/[(1+z)(1-4z+2z^2)^2].
%e A181337 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 2-compositions are written as (top row / bottom row)) we have 1+0+1+1+1+0+2=6 even entries.
%p A181337 g := z*(1-z)^2*(1+z-z^2)/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 28): seq(coeff(gser, z, n), n = 0 .. 25);
%Y A181337 Cf. A181305, A181336.
%K A181337 nonn,easy
%O A181337 0,3
%A A181337 _Emeric Deutsch_, Oct 14 2010