A181337 - OEIS

%I #4 Jul 24 2022 13:58:12

%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 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 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 L-convex polyominoes, European Journal of Combinatorics, 28, 2007, 1724-1741.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12,-4,12,-4).

%F G.f. = z(1+z-z^2)(1-z)^2/[(1+z)(1-4z+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 2-compositions are written as (top row / bottom row)) we have 1+0+1+1+1+0+2=6 even entries.

%p 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 Cf. A181305, A181336.

%K nonn,easy

%O 0,3

%A _Emeric Deutsch_, Oct 14 2010