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 A256317 #10 Apr 12 2018 11:55:54
%S A256317 0,0,2,11,35,90,199,391,709,1206,1945,3009,4494,6510,9192,12692,17180,
%T A256317 22856,29941,38677,49342,62239,77695,96079,117788,143247,172929,
%U A256317 207338,247010,292534,344534,403670,470660,546261,631269,726544,832989,951549,1083239
%N A256317 Number of partitions of 4n into exactly 6 parts.
%H A256317 Colin Barker, <a href="/A256317/b256317.txt">Table of n, a(n) for n = 0..1000</a>
%H A256317 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).
%F A256317 G.f.: x^2*(x+1)^2*(x^2+1)*(x^4+2*x^3+2*x^2+x+2) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)).
%e A256317 For n=2 the 2 partitions of 4*2 = 8 are [1,1,1,1,1,3] and [1,1,1,1,2,2].
%t A256317 Table[Length[IntegerPartitions[4n,{6}]],{n,0,40}] (* or *) LinearRecurrence[ {3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1},{0,0,2,11,35,90,199,391,709,1206,1945,3009,4494,6510},40] (* _Harvey P. Dale_, Apr 12 2018 *)
%o A256317 (PARI) concat(0, vector(40, n, k=0; forpart(p=4*n, k++, , [6,6]); k))
%o A256317 (PARI) concat([0,0], Vec(x^2*(x+1)^2*(x^2+1)*(x^4+2*x^3+2*x^2+x+2) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)) + O(x^100)))
%Y A256317 Cf. A238340 (4 parts), A256316 (5 parts).
%K A256317 nonn,easy
%O A256317 0,3
%A A256317 _Colin Barker_, Mar 23 2015