This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A181331 #11 Jul 24 2022 14:10:38
%S A181331 0,1,5,23,99,408,1632,6388,24596,93488,351664,1311536,4856432,
%T A181331 17873408,65436544,238480960,865665600,3131196672,11290210560,
%U A181331 40594476800,145588087552,520933746688,1860059009024,6628828632064,23582036472832
%N A181331 Number of 0's in the top rows of all 2-compositions of n.
%C A181331 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.
%H A181331 G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, <a href="http://dx.doi.org/10.1016/j.ejc.2006.06.020">Combinatorial aspects of L-convex polyominoes</a>, European J. Combin. 28 (2007), no. 6, 1724-1741.
%H A181331 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16,-4).
%F A181331 a(n) = Sum_{k=0..n} A181330(n,k).
%F A181331 a(n) = (1/2)*A181294(n).
%F A181331 G.f.: x*(1 - x)^3 / (1 - 4*x + 2*x^2)^2.
%F A181331 a(n) = A181292(n)-2*A181292(n-1)+A181292(n-2). - _R. J. Mathar_, Jul 24 2022
%e A181331 a(2)=5 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=5 zeros.
%p A181331 g := z*(1-z)^3/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 27);
%t A181331 LinearRecurrence[{8, -20, 16, -4}, {0, 1, 5, 23, 99}, 25] (* _Georg Fischer_, Feb 01 2021 *)
%Y A181331 Cf. A181330, A181294.
%K A181331 nonn
%O A181331 0,3
%A A181331 _Emeric Deutsch_, Oct 13 2010