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 A027053 #35 Sep 08 2022 08:44:49
%S A027053 1,4,9,18,35,66,123,228,421,776,1429,2630,4839,8902,16375,30120,55401,
%T A027053 101900,187425,344730,634059,1166218,2145011,3945292,7256525,13346832,
%U A027053 24548653,45152014,83047503,152748174,280947695,516743376
%N A027053 a(n) = T(n,n+2), T given by A027052.
%C A027053 Second differences of (A027026(n)-1)/2.
%C A027053 Pairwise sums of A089068.
%C A027053 a(n) is also the number of fixed polyominoes with n cells of height (or width) 2. - _David Bevan_, Sep 09 2009
%H A027053 G. C. Greubel, <a href="/A027053/b027053.txt">Table of n, a(n) for n = 2..1001</a>
%H A027053 Doron Zeilberger, The <a href="http://www.math.rutgers.edu/~zeilberg/TM/oani1"> generating functions</a> and <a href="http://www.math.rutgers.edu/~zeilberg/TM/oani2">series expansions</a> for 2D lattice-animals of globally bounded width. [Local copies of <a href="/A027053/a027053.txt">generating functions</a> and <a href="/A027053/a027053_1.txt">series expansions</a>].
%H A027053 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>
%H A027053 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1).
%F A027053 G.f.: x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3)).
%F A027053 a(n) = A089068(n-1) + A089068(n).
%F A027053 a(n) = a(n-1) + a(n-2) + a(n-3) + 4. - _David Bevan_, Sep 09 2009
%F A027053 a(n) = A001590(n+3) - 2. - _David Bevan_, Sep 09 2009
%F A027053 a(n+1) - a(n) = A000213(n+1). - _R. J. Mathar_, Aug 04 2013
%p A027053 seq(coeff(series(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3)), x, n+1), x, n), n = 2 ..30); # _G. C. Greubel_, Nov 05 2019
%t A027053 LinearRecurrence[{2,0,0,-1}, {1,4,9,18}, 30] (* _G. C. Greubel_, Nov 05 2019 *)
%o A027053 (PARI) my(x='x+O('x^32)); Vec(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3))) \\ _G. C. Greubel_, Nov 05 2019
%o A027053 (Magma) R<x>:=PowerSeriesRing(Integers(), 32); Coefficients(R!( x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3)) )); // _G. C. Greubel_, Nov 05 2019
%o A027053 (Sage)
%o A027053 def A027053_list(prec):
%o A027053 P.<x> = PowerSeriesRing(ZZ, prec)
%o A027053 return P(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3))).list()
%o A027053 a=A027053_list(32); a[2:] # _G. C. Greubel_, Nov 05 2019
%o A027053 (GAP) a:=[1,4,9,18];; for n in [5..30] do a[n]:=2*a[n-1]-a[n-4]; od; a; # _G. C. Greubel_, Nov 05 2019
%Y A027053 2nd column of A308359.
%K A027053 nonn,easy
%O A027053 2,2
%A A027053 _Clark Kimberling_