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 A242727 #28 Sep 08 2022 08:46:08
%S A242727 1,7,29,86,198,396,719,1203,1899,2866,4156,5840,7997,10695,14025,
%T A242727 18086,22962,28764,35611,43603,52871,63554,75768,89664,105401,123111,
%U A242727 142965,165142,189790,217100,247271,280467,316899,356786,400308,447696,499189,554983
%N A242727 Sum of the third largest parts of the partitions of 4n into 4 parts.
%H A242727 A. Osorio, <a href="http://mpra.ub.uni-muenchen.de/56690/1/MPRA_paper_56690.pdf">A Sequential Allocation Problem: The Asymptotic Distribution of Resources</a>, Munich Personal RePEc Archive, 2014.
%H A242727 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A242727 <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 A242727 G.f.: (1 + 4*x + 11*x^2 + 17*x^3 + 12*x^4 + 9*x^5 + 2*x^6) / ((1 - x)^5*(1 + x + x^2)^2).
%F A242727 a(n) = A238328(n) - A239667(n) - A241084(n) - A238702(n).
%F A242727 a(n) = 7/27*n^4 + 35/27*n^3 + 22/9*n^2 + 59/27*n + O(1). - _Ralf Stephan_, May 26 2014
%e A242727 Add the numbers in the third column for a(n):
%e A242727 13+ 1 + 1 + 1
%e A242727 12+ 2 + 1 + 1
%e A242727 11+ 3 + 1 + 1
%e A242727 10+ 4 + 1 + 1
%e A242727 9 + 5 + 1 + 1
%e A242727 8 + 6 + 1 + 1
%e A242727 7 + 7 + 1 + 1
%e A242727 11+ 2 + 2 + 1
%e A242727 10+ 3 + 2 + 1
%e A242727 9 + 4 + 2 + 1
%e A242727 8 + 5 + 2 + 1
%e A242727 7 + 6 + 2 + 1
%e A242727 9 + 3 + 3 + 1
%e A242727 8 + 4 + 3 + 1
%e A242727 7 + 5 + 3 + 1
%e A242727 6 + 6 + 3 + 1
%e A242727 7 + 4 + 4 + 1
%e A242727 6 + 5 + 4 + 1
%e A242727 5 + 5 + 5 + 1
%e A242727 9 + 1 + 1 + 1 10+ 2 + 2 + 2
%e A242727 8 + 2 + 1 + 1 9 + 3 + 2 + 2
%e A242727 7 + 3 + 1 + 1 8 + 4 + 2 + 2
%e A242727 6 + 4 + 1 + 1 7 + 5 + 2 + 2
%e A242727 5 + 5 + 1 + 1 6 + 6 + 2 + 2
%e A242727 7 + 2 + 2 + 1 8 + 3 + 3 + 2
%e A242727 6 + 3 + 2 + 1 7 + 4 + 3 + 2
%e A242727 5 + 4 + 2 + 1 6 + 5 + 3 + 2
%e A242727 5 + 3 + 3 + 1 6 + 4 + 4 + 2
%e A242727 4 + 4 + 3 + 1 5 + 5 + 4 + 2
%e A242727 5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
%e A242727 4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
%e A242727 3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
%e A242727 3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
%e A242727 1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
%e A242727 4(1) 4(2) 4(3) 4(4) .. 4n
%e A242727 ------------------------------------------------------------------------
%e A242727 1 7 29 86 .. a(n)
%t A242727 CoefficientList[Series[-(1 + 4x + 11x^2 + 17x^3 + 12x^4 + 9x^5 + 2x^6) / ((-1 + x)^5 (1 + x + x^2)^2), {x, 0, 50}], x]
%t A242727 LinearRecurrence[{3, -3, 3, -6, 6, -3, 3, -3, 1}, {1, 7, 29, 86, 198, 396, 719, 1203, 1899}, 50] (* _Vincenzo Librandi_, Aug 29 2015 *)
%o A242727 (Magma) I:=[1,7,29,86,198,396,719,1203,1899]; [n le 9 select I[n] else 3*Self(n-1)-3*Self(n-2)+3*Self(n-3)-6*Self(n-4)+6*Self(n-5)-3*Self(n-6)+3*Self(n-7)-3*Self(n-8)+Self(n-9): n in [1..40]]; // _Vincenzo Librandi_, Aug 29 2015
%Y A242727 Cf. A238328, A238340, A238702, A239667, A241084.
%K A242727 nonn,easy
%O A242727 1,2
%A A242727 _Wesley Ivan Hurt_ and _Antonio Osorio_, May 21 2014