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 A236370 #34 Nov 19 2021 17:55:11
%S A236370 1,9,34,81,163,282,454,678,973,1335,1786,2319,2959,3696,4558,5532,
%T A236370 6649,7893,9298,10845,12571,14454,16534,18786,21253,23907,26794,29883,
%U A236370 33223,36780,40606,44664,49009,53601,58498,63657,69139,74898,80998,87390,94141
%N A236370 Sum of the largest parts in the partitions of 3n into 3 parts.
%H A236370 Vincenzo Librandi, <a href="/A236370/b236370.txt">Table of n, a(n) for n = 1..1000</a>
%H A236370 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A236370 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A236370 a(n) = 3n * (n^2 - floor(n^2/4)) - Sum_{i=1..n} (2*i^2 - floor(i^2/4)) - Sum_{i=1..floor((n-1)/2)} (n + i) * (n - 2i).
%F A236370 From _Colin Barker_, Jan 24 2014: (Start)
%F A236370 a(n) = (-1+(-1)^n-(1+3*(-1)^n)*n-6*n^2+22*n^3)/16.
%F A236370 G.f.: x*(2*x^4+8*x^3+15*x^2+7*x+1) / ((x-1)^4*(x+1)^2). (End)
%F A236370 a(n) = Sum_{j=0..n-2} (Sum_{i=n+1+floor(j/2)-floor(1/j+1)..n+2*(j+1)} i), n > 1. - _Wesley Ivan Hurt_, Feb 10 2014
%F A236370 a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6). - _Wesley Ivan Hurt_, Nov 19 2021
%e A236370 Add first columns for a(n)..
%e A236370 13 + 1 + 1
%e A236370 12 + 2 + 1
%e A236370 11 + 3 + 1
%e A236370 10 + 4 + 1
%e A236370 9 + 5 + 1
%e A236370 8 + 6 + 1
%e A236370 7 + 7 + 1
%e A236370 10 + 1 + 1 11 + 2 + 2
%e A236370 9 + 2 + 1 10 + 3 + 2
%e A236370 8 + 3 + 1 9 + 4 + 2
%e A236370 7 + 4 + 1 8 + 5 + 2
%e A236370 6 + 5 + 1 7 + 6 + 2
%e A236370 7 + 1 + 1 8 + 2 + 2 9 + 3 + 3
%e A236370 6 + 2 + 1 7 + 3 + 2 8 + 4 + 3
%e A236370 5 + 3 + 1 6 + 4 + 2 7 + 5 + 3
%e A236370 4 + 4 + 1 5 + 5 + 2 6 + 6 + 3
%e A236370 4 + 1 + 1 5 + 2 + 2 6 + 3 + 3 7 + 4 + 4
%e A236370 3 + 2 + 1 4 + 3 + 2 5 + 4 + 3 6 + 5 + 4
%e A236370 1 + 1 + 1 2 + 2 + 2 3 + 3 + 3 4 + 4 + 4 5 + 5 + 5
%e A236370 3(1) 3(2) 3(3) 3(4) 3(5) .. 3n
%e A236370 ---------------------------------------------------------------------
%e A236370 1 9 34 81 163 .. a(n)
%t A236370 Table[3 n (n^2 - Floor[n^2/4]) - Sum[2 i^2 - Floor[i^2/4], {i, n}] -
%t A236370 Sum[(n + i) (n - 2 i), {i, Floor[(n - 1)/2]}], {n, 100}]
%t A236370 LinearRecurrence[{2,1,-4,1,2,-1},{1,9,34,81,163,282},50] (* _Harvey P. Dale_, Nov 11 2017 *)
%o A236370 (PARI) Vec(x*(2*x^4+8*x^3+15*x^2+7*x+1)/((x-1)^4*(x+1)^2) + O(x^100)) \\ _Colin Barker_, Jan 24 2014
%Y A236370 Cf. A019298, A235988, A236364, A236758, A236762, A237264.
%K A236370 nonn,easy
%O A236370 1,2
%A A236370 _Wesley Ivan Hurt_, Jan 23 2014