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 A181367 #6 Jul 22 2022 12:26:34
%S A181367 2,6,22,78,272,940,3232,11080,37920,129648,443008,1513248,5168000,
%T A181367 17647552,60258304,205746304,702484992,2398480128,8189016064,
%U A181367 27959235072,95459170304,325918735360,1112757649408,3799195224064
%N A181367 Number of 2-compositions of n containing at least one 0 entry. 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 A181367 a(n)=A181365(n,0).
%D A181367 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 A181367 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,4).
%F A181367 G.f.=2z(1-z)^3/[(1-2z)(1-4z+2z^2)].
%F A181367 4*a(n) = 2*A007070(n)-2^n, n>1. - _R. J. Mathar_, Jul 22 2022
%e A181367 a(2)=6 because the 2-compositions of 2, written as (top row / bottom row), are (1/1), (0/2), (2/0), (1,0/0,1), (0,1/1,0), (1,1/0,0), (0,0/1,1) and only the first one does not contain a 0 entry.
%p A181367 G := 2*z*(1-z)^3/((1-2*z)*(1-4*z+2*z^2)): Gser := series(G, z = 0, 30): seq(coeff(Gser, z, n), n = 1 .. 25);
%t A181367 CoefficientList[Series[(2x (1-x)^3)/((1-2x)(1-4x+2x^2)),{x,0,30}],x] (* _Harvey P. Dale_, Mar 29 2020 *)
%Y A181367 Cf. A181365
%K A181367 nonn,easy
%O A181367 1,1
%A A181367 _Emeric Deutsch_, Oct 15 2010