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 A243011 #39 Jun 20 2024 20:36:37
%S A243011 3,34,159,489,1161,2365,4336,7323,11640,17646,25702,36246,49761,66720,
%T A243011 87685,113263,144039,180699,223974,274561,333270,400956,478428,566620,
%U A243011 666511,779022,905211,1046181,1202965,1376745,1568748,1780119,2012164,2266234,2543586
%N A243011 Sum of the three largest parts in the partitions of 4n into 4 parts.
%H A243011 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A243011 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-6,6,-3,3,-3,1).
%F A243011 a(n) = A238328(n) - A238702(n).
%F A243011 a(n) = A239667(n) + A241084(n) + A242727(n).
%F A243011 a(n) = 4n * A238340(n) - Sum_{i=1..n} A238340(i).
%F A243011 a(n) = (4n-1) * A238702(n) - 4n * A238702(n-1), n > 1.
%F A243011 a(n) = A238328(n) - (1/4) * Sum_{i=1..n} A238328(i)/i.
%F A243011 G.f.: -x*(16*x^6+58*x^5+87*x^4+105*x^3+66*x^2+25*x+3) / ((x-1)^5*(x^2+x+1)^2). - _Colin Barker_, Sep 22 2014
%F A243011 a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 6*a(n-4) + 6*a(n-5) - 3*a(n-6) + 3*a(n-7) - 3*a(n-8) + a(n-9). - _Wesley Ivan Hurt_, Jun 20 2024
%e A243011 Add up the numbers in the first three columns for a(n):
%e A243011 13 + 1 + 1 + 1
%e A243011 12 + 2 + 1 + 1
%e A243011 11 + 3 + 1 + 1
%e A243011 10 + 4 + 1 + 1
%e A243011 9 + 5 + 1 + 1
%e A243011 8 + 6 + 1 + 1
%e A243011 7 + 7 + 1 + 1
%e A243011 11 + 2 + 2 + 1
%e A243011 10 + 3 + 2 + 1
%e A243011 9 + 4 + 2 + 1
%e A243011 8 + 5 + 2 + 1
%e A243011 7 + 6 + 2 + 1
%e A243011 9 + 3 + 3 + 1
%e A243011 8 + 4 + 3 + 1
%e A243011 7 + 5 + 3 + 1
%e A243011 6 + 6 + 3 + 1
%e A243011 7 + 4 + 4 + 1
%e A243011 6 + 5 + 4 + 1
%e A243011 5 + 5 + 5 + 1
%e A243011 9 + 1 + 1 + 1 10 + 2 + 2 + 2
%e A243011 8 + 2 + 1 + 1 9 + 3 + 2 + 2
%e A243011 7 + 3 + 1 + 1 8 + 4 + 2 + 2
%e A243011 6 + 4 + 1 + 1 7 + 5 + 2 + 2
%e A243011 5 + 5 + 1 + 1 6 + 6 + 2 + 2
%e A243011 7 + 2 + 2 + 1 8 + 3 + 3 + 2
%e A243011 6 + 3 + 2 + 1 7 + 4 + 3 + 2
%e A243011 5 + 4 + 2 + 1 6 + 5 + 3 + 2
%e A243011 5 + 3 + 3 + 1 6 + 4 + 4 + 2
%e A243011 4 + 4 + 3 + 1 5 + 5 + 4 + 2
%e A243011 5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
%e A243011 4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
%e A243011 3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
%e A243011 3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
%e A243011 1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
%e A243011 4(1) 4(2) 4(3) 4(4) .. 4n
%e A243011 ------------------------------------------------------------------------
%e A243011 3 34 159 489 .. a(n)
%t A243011 a[1] = 4; a[n_] := (n/(n - 1)) a[n - 1] + 4 n*Sum[(Floor[(4 n - 2 - i)/2] - i) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[a[n] - Sum[a[i]/i, {i, n}]/4, {n, 30}]
%o A243011 (PARI) Vec(-x*(16*x^6+58*x^5+87*x^4+105*x^3+66*x^2+25*x+3)/((x-1)^5*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 22 2014
%Y A243011 Cf. A238328, A238340, A238702, A239667, A241084.
%K A243011 nonn,easy
%O A243011 1,1
%A A243011 _Wesley Ivan Hurt_, May 28 2014