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 A256320 #18 Jun 07 2016 02:58:54
%S A256320 0,1,5,12,21,33,48,65,85,108,133,161,192,225,261,300,341,385,432,481,
%T A256320 533,588,645,705,768,833,901,972,1045,1121,1200,1281,1365,1452,1541,
%U A256320 1633,1728,1825,1925,2028,2133,2241,2352,2465,2581,2700,2821,2945,3072,3201
%N A256320 Number of partitions of 4n into exactly 3 parts.
%H A256320 Colin Barker, <a href="/A256320/b256320.txt">Table of n, a(n) for n = 0..1000</a>
%H A256320 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A256320 a(n) = A184637(n) for n > 2.
%F A256320 a(n) = 2*a(n-1)-a(n-2)+a(n-3)-2*a(n-4)+a(n-5) for n>4.
%F A256320 G.f.: -x*(x+1)^3 / ((x-1)^3*(x^2+x+1)).
%F A256320 a(n) = 2*(6*n^2+cos((2*Pi*n)/3)-1)/9. - _Colin Barker_, Jun 06 2016
%e A256320 For n=2 the 5 partitions of 4*2 = 8 are [1,1,6], [1,2,5], [1,3,4], [2,2,4] and [2,3,3].
%t A256320 Length /@ (Total /@ IntegerPartitions[4 #, {3}] & /@ Range[0, 49]) (* _Michael De Vlieger_, Mar 24 2015 *)
%t A256320 CoefficientList[Series[-x (x + 1)^3/((x - 1)^3 (x^2 + x + 1)), {x, 0, 49}], x] (* or *)
%t A256320 Table[2 (6 n^2 + Cos[(2 Pi n)/3] - 1)/9, {n, 0, 49}] (* _Michael De Vlieger_, Jun 06 2016 *)
%o A256320 (PARI) concat(0, vector(40, n, k=0; forpart(p=4*n, k++, , [3,3]); k))
%o A256320 (PARI) concat(0, Vec(-x*(x+1)^3/((x-1)^3*(x^2+x+1)) + O(x^100)))
%Y A256320 Cf. A033428 (6n), A256321 (5n), A256322 (7n).
%Y A256320 Cf. A184637.
%K A256320 nonn,easy
%O A256320 0,3
%A A256320 _Colin Barker_, Mar 24 2015