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 A185395 #28 May 10 2025 03:20:27
%S A185395 0,0,0,1,3,3,4,9,9,9,18,18,16,30,30,25,45,45,36,63,63,49,84,84,64,108,
%T A185395 108,81,135,135,100,165,165,121,198,198,144,234,234,169,273,273,196,
%U A185395 315,315,225,360,360,256
%N A185395 a(3n) = n^2, a(3n+1) = a(3n+2) = 3*n*(n+1)/2.
%C A185395 Expansion of ((x+x^2)/(1-x^3))^k with k = 3 ; for k = 1 see A011655, for k = 2 see A186731, for k = 4 see A185292.
%H A185395 G. C. Greubel, <a href="/A185395/b185395.txt">Table of n, a(n) for n = 0..1000</a>
%H A185395 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3,0,0,-3,0,0,1).
%F A185395 G.f.: (x*(1+x)/(1-x^3))^3.
%F A185395 From _Amiram Eldar_, May 10 2025: (Start)
%F A185395 Sum_{n>=3} 1/a(n) = Pi^2/6 + 4/3.
%F A185395 Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/12 (A072691). (End)
%t A185395 LinearRecurrence[{0,0,3,0,0,-3,0,0,1},{0,0,0,1,3,3,4,9,9},50] (* _Harvey P. Dale_, Jan 23 2013 *)
%o A185395 (PARI) x='x+O('x^50); concat([0, 0, 0], Vec((x*(1+x)/(1-x^3))^3)) \\ _G. C. Greubel_, Jun 29 2017
%Y A185395 Column k = 3 of triangle in A198295.
%Y A185395 Cf. A000217, A000290, A011655, A045943, A072691, A186731, A185292.
%K A185395 easy,nonn
%O A185395 0,5
%A A185395 _Philippe Deléham_, Jan 21 2012