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 A008742 #46 Sep 08 2022 08:44:36
%S A008742 1,0,1,1,2,1,4,2,5,4,7,5,10,7,12,10,15,12,19,15,22,19,26,22,31,26,35,
%T A008742 31,40,35,46,40,51,46,57,51,64,57,70,64,77,70,85,77,92,85,100,92,109,
%U A008742 100,117,109,126,117,136
%N A008742 Molien series for 3-dimensional group [3,3 ]+ = 332.
%C A008742 a(n) is also the number of integer-sided triangles having perimeter n + 3, modulo rotations but not reflections. - _James East_, Oct 16 2017
%H A008742 Vincenzo Librandi, <a href="/A008742/b008742.txt">Table of n, a(n) for n = 0..1000</a>
%H A008742 James East and Ron Niles, <a href="https://arxiv.org/abs/1710.11245">Integer polygons with given perimeter</a>, arXiv/1710.11245 [math.CO], 2017.
%H A008742 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H A008742 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,-1,-2,0,1).
%F A008742 G.f.: (1+x^6)/((1-x^2)*(1-x^3)*(1-x^4)).
%F A008742 a(n) ~ 1/24*n^2. - _Ralf Stephan_, Apr 29 2014
%F A008742 a(n) = 1 - 19*n/24 - 5*n^2/24 + 4/3*floor(n/3) + (n/2+3/4)*floor(n/2) + 2/3*floor((n+1)/3). - _Vaclav Kotesovec_, Apr 29 2014
%F A008742 a(n) = floor((n^2+3*n+20)/24+(2*n+3)*(-1)^n/16). - _Tani Akinari_, Jun 20 2014
%F A008742 G.f.: (1-x^2+x^4)/((1+x+x^2)*(1+x)^2*(1-x)^3). - _R. J. Mathar_, Dec 18 2014
%e A008742 For n = 6, there are 4 rotation-classes of perimeter-9 triangles: 441, 432, 423, 333. Note that 432 and 423 are reflections of each other, but these are not rotationally equivalent. So a(6) = 4. - _James East_, Oct 16 2017
%t A008742 CoefficientList[Series[(1+x^6)/((1-x^2)*(1-x^3)*(1-x^4)), {x, 0, 60}], x] (* _Vaclav Kotesovec_, Apr 29 2014 *)
%o A008742 (PARI) my(x='x+O('x^60)); Vec((1+x^6)/((1-x^2)*(1-x^3)*(1-x^4))) \\ _G. C. Greubel_, Aug 03 2019
%o A008742 (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^6)/((1-x^2)*(1-x^3)*(1-x^4)) )); // _G. C. Greubel_, Aug 03 2019
%o A008742 (Sage) ((1+x^6)/((1-x^2)*(1-x^3)*(1-x^4))).series(x, 60).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 03 2019
%o A008742 (GAP) a:=[1,0,1,1,2,1,4];; for n in [8..60] do a[n]:=2*a[n-2]+a[n-3]-a[n-4] -2*a[n-5]+a[n-7]; od; a; # _G. C. Greubel_, Aug 03 2019
%Y A008742 Cf. A005044, A293819 (k-gon triangle), A293820 (polygons), A293821 (quadrilaterals), A293822 (pentagons), A293823 (hexagons)
%K A008742 nonn,easy
%O A008742 0,5
%A A008742 _N. J. A. Sloane_