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 A181290 #9 Apr 06 2025 08:47:24
%S A181290 0,2,11,52,227,944,3800,14944,57748,220128,829968,3101376,11502704,
%T A181290 42393088,155392768,566918144,2059768384,7456496128,26905720576,
%U A181290 96804463616,347386161920,1243665567744,4442849839104,15840448094208,56375692407808,200307512532992,710622022258688,2517475213557760
%N A181290 The sum of the lengths of 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. The length of the 2-composition is the number of columns.
%H A181290 G. Castiglione, A. Frosini, E. Munarini, A. Restivo, and S. Rinaldi, <a href="https://doi.org/10.1016/j.ejc.2006.06.020">Combinatorial aspects of L-convex polyominoes</a>, European Journal of Combinatorics, 28 (2007), 1724-1741.
%H A181290 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16,-4).
%F A181290 a(n) = Sum_{k=0..n} k * A181289(n,k).
%F A181290 G.f.: z*(2-z)*(1-z)^2/(1-4*z+2*z^2)^2.
%p A181290 g := z*(1-z)^2*(2-z)/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 28): seq(coeff(gser, z, n), n = 0 .. 25);
%Y A181290 Cf. A181289.
%K A181290 nonn,easy
%O A181290 0,2
%A A181290 _Emeric Deutsch_, Oct 12 2010