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 A181300 #6 Apr 05 2023 10:56:56
%S A181300 0,0,1,4,19,80,328,1304,5084,19512,73976,277688,1033848,3822584,
%T A181300 14050824,51385720,187095240,678570360,2452626312,8837584248,
%U A181300 31756892552,113831195000,407102551688,1452956457336,5175872174728
%N A181300 Number of columns with top entry equal to bottom entry 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 A181300 a(n)=Sum(k*A181299(n,k),k>=0).
%D A181300 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 A181300 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12,-4,12,-4).
%F A181300 G.f. = z^2*(1-z)^3/[(1+z)(1-4z+2z^2)^2].
%p A181300 g := z^2*(1-z)^3/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 27);
%t A181300 LinearRecurrence[{7,-12,-4,12,-4},{0,0,1,4,19,80},30] (* _Harvey P. Dale_, Apr 05 2023 *)
%Y A181300 Cf. A181299
%K A181300 nonn,easy
%O A181300 0,4
%A A181300 _Emeric Deutsch_, Oct 12 2010