cp's OEIS Frontend

A181328 Number of columns with an even 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 A181328 #5 Jul 24 2022 14:23:02
%S A181328 0,0,3,12,59,248,1024,4080,15948,61312,232792,874864,3260360,12064928,
%T A181328 44378984,162399504,591613880,2146724864,7762397576,27980907248,
%U A181328 100580448920,360636908000,1290131211432,4605675085008,16410645183928
%N A181328 Number of columns with an even 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 A181328 a(n)=Sum(A181327(n,k), k>=0).
%D A181328 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 A181328 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5,-16,8,8,-4).
%F A181328 G.f. = z^2*(1-z)^2*(3-z^2)/[(1+z)(1-4z+2z^2)]^2.
%F A181328 a(n) = (3*A181326(n-1) -A181326(n-3))/2. - _R. J. Mathar_, Jul 24 2022
%e A181328 a(2)=3 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+1+1+0+0+0+0=3 columns with even sums.
%p A181328 g := z^2*(1-z)^2*(3-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 A181328 Cf. A181327, A181326
%K A181328 nonn
%O A181328 0,3
%A A181328 _Emeric Deutsch_, Oct 13 2010