cp's OEIS Frontend

A181326 Number of columns with an odd sum in 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 A181326 #4 Jul 24 2022 14:16:02
%S A181326 0,2,8,40,168,696,2776,10864,41800,158816,597176,2226512,8242344,
%T A181326 30328160,111013784,404518640,1468154504,5309771264,19143323000,
%U A181326 68823556368,246805713000,883028659744,3152718627672,11234773009200
%N A181326 Number of columns with an odd sum in 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 A181326 a(n)=Sum(A181308(n,k), k=0..n).
%C A181326 For the "even sum" case, see A181328.
%D A181326 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 A181326 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5,-16,8,8,-4).
%F A181326 G.f. = 2z(1-z)^2/[(1+z)(1-4z+2z^2)]^2.
%e A181326 a(2)=8 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 0+0+0+2+2+2+2=8 columns with odd sums.
%p A181326 g := 2*z*(1-z)^2/((1+z)^2*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 27);
%Y A181326 Cf. A181308, A181327, A181328
%K A181326 nonn,easy
%O A181326 0,2
%A A181326 _Emeric Deutsch_, Oct 13 2010