cp's OEIS Frontend

A181298 The number of even entries in all the 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 A181298 #4 Jul 26 2022 13:24:45
%S A181298 0,2,12,56,246,1024,4128,16248,62832,239640,903944,3379064,12536552,
%T A181298 46215672,169443592,618303864,2246863624,8135066488,29358346888,
%U A181298 105642047864,379143054472,1357496762744,4849952390792,17293404551544
%N A181298 The number of even entries in all the 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 A181298 a(n)=Sum(k*A181297(n,k),k=0..n).
%D A181298 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 A181298 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12,-4,12,-4).
%F A181298 G.f. = 2z(1-z)^2*(1+z-z^2)/[(1+z)(1-4z+2z^2)^2].
%F A181298 a(n) = 2*A181337(n). - _R. J. Mathar_, Jul 26 2022
%e A181298 a(2)=12 because in the 2-compositions of 2, namely (1/1),(0/2),(2/0),(1,0/0,1),(0,1/1,0),(1,1/0,0), and (0,0/1,1), we have 0+2+2+2+2+2+2=12 odd entries (the 2-compositions are written as (top row/bottom row)).
%p A181298 g := 2*z*(1-z)^2*(1+z-z^2)/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 25);
%Y A181298 Cf. A181295, A181296, A181297.
%K A181298 nonn,easy
%O A181298 0,2
%A A181298 _Emeric Deutsch_, Oct 12 2010