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 A195321 #45 Dec 02 2024 10:10:00
%S A195321 0,18,72,162,288,450,648,882,1152,1458,1800,2178,2592,3042,3528,4050,
%T A195321 4608,5202,5832,6498,7200,7938,8712,9522,10368,11250,12168,13122,
%U A195321 14112,15138,16200,17298,18432,19602,20808,22050,23328,24642,25992,27378,28800,30258,31752
%N A195321 a(n) = 18*n^2.
%C A195321 Sequence found by reading the line from 0, in the direction 0, 18, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Semi-axis opposite to A195316 in the same spiral.
%C A195321 Area of a square with diagonal 6n. - _Wesley Ivan Hurt_, Jun 19 2014
%C A195321 Number of identical tessellation tiles that are composed of 48 equilateral edge joined triangles that can be formed into a order n hexagon. The example tiles shown in the link below are tessellated with eight sphinx tiles. See A291582. - _Craig Knecht_, Sep 02 2017
%H A195321 Vincenzo Librandi, <a href="/A195321/b195321.txt">Table of n, a(n) for n = 0..10000</a>
%H A195321 Craig Knecht, <a href="/A195321/a195321.png">Hexagon tessellation</a>.
%H A195321 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195321 a(n) = 18*A000290(n) = 9*A001105(n) = 6*A033428(n) = 3*A033581(n) = 2*A016766(n).
%F A195321 G.f.: 18*x*(1+x)/(1-x)^3. - _Wesley Ivan Hurt_, Jun 20 2014
%F A195321 From _Elmo R. Oliveira_, Dec 01 2024: (Start)
%F A195321 E.g.f.: 18*x*(1 + x)*exp(x).
%F A195321 a(n) = n*A008600(n) = A195147(2*n).
%F A195321 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%p A195321 A195321:=n->18*n^2; seq(A195321(n), n=0..50); # _Wesley Ivan Hurt_, Jun 19 2014
%t A195321 18 Range[0, 50]^2 (* or *) CoefficientList[Series[18 x*(1 + x)/(1 - x)^3, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jun 20 2014 *)
%t A195321 LinearRecurrence[{3,-3,1},{0,18,72},50] (* _Harvey P. Dale_, Mar 26 2023 *)
%o A195321 (Magma)[18*n^2:n in [0..40]]; // _Vincenzo Librandi_, Sep 20 2011
%o A195321 (PARI) a(n)=18*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A195321 Bisection of A195147.
%Y A195321 Cf. A016802, A033581, A033583, A135453, A139098, A144555, A195322, A195323.
%Y A195321 Cf. A000290, A001105, A008600, A016766, A033428, A195160, A195316, A291582.
%K A195321 nonn,easy
%O A195321 0,2
%A A195321 _Omar E. Pol_, Sep 16 2011