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 A239667 #34 Sep 08 2022 08:46:07
%S A239667 1,17,84,262,629,1289,2370,4014,6393,9703,14150,19974,27439,36815,
%T A239667 48410,62556,79587,99879,123832,151844,184359,221845,264764,313628,
%U A239667 368973,431325,501264,579394,666305,762645,869086,986282,1114949,1255827,1409634,1577154,1759195,1956539,2170038,2400568
%N A239667 Sum of the largest parts of the partitions of 4n into 4 parts.
%H A239667 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 A239667 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A239667 <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 A239667 G.f.: -x*(9*x^6+32*x^5+50*x^4+58*x^3+36*x^2+14*x+1) / ((x-1)^5*(x^2+x+1)^2). - _Colin Barker_, Mar 23 2014
%F A239667 Let b(1) = 4, with b(n) = (n/(n-1)) * b(n-1) + 4n * Sum_{i=0..2n} (floor((4n-2-i)/2)-i) * floor((sign(floor((4n-2-i)/2)-i)+2)/2). Then a(1) = 1, with a(n) = a(n-1) + b(n-1)/(4n-4) + Sum_{i=j+1..floor((4n-2-j)/2)} ( Sum_{j=0..2n} (4n-2-i-j) * floor((sign(floor((4n-2-j)/2)-j)+2)/2) ). - _Wesley Ivan Hurt_, Jun 13 2014
%e A239667 Add the numbers in the first column for a(n):
%e A239667 13 + 1 + 1 + 1
%e A239667 12 + 2 + 1 + 1
%e A239667 11 + 3 + 1 + 1
%e A239667 10 + 4 + 1 + 1
%e A239667 9 + 5 + 1 + 1
%e A239667 8 + 6 + 1 + 1
%e A239667 7 + 7 + 1 + 1
%e A239667 11 + 2 + 2 + 1
%e A239667 10 + 3 + 2 + 1
%e A239667 9 + 4 + 2 + 1
%e A239667 8 + 5 + 2 + 1
%e A239667 7 + 6 + 2 + 1
%e A239667 9 + 3 + 3 + 1
%e A239667 8 + 4 + 3 + 1
%e A239667 7 + 5 + 3 + 1
%e A239667 6 + 6 + 3 + 1
%e A239667 7 + 4 + 4 + 1
%e A239667 6 + 5 + 4 + 1
%e A239667 5 + 5 + 5 + 1
%e A239667 9 + 1 + 1 + 1 10 + 2 + 2 + 2
%e A239667 8 + 2 + 1 + 1 9 + 3 + 2 + 2
%e A239667 7 + 3 + 1 + 1 8 + 4 + 2 + 2
%e A239667 6 + 4 + 1 + 1 7 + 5 + 2 + 2
%e A239667 5 + 5 + 1 + 1 6 + 6 + 2 + 2
%e A239667 7 + 2 + 2 + 1 8 + 3 + 3 + 2
%e A239667 6 + 3 + 2 + 1 7 + 4 + 3 + 2
%e A239667 5 + 4 + 2 + 1 6 + 5 + 3 + 2
%e A239667 5 + 3 + 3 + 1 6 + 4 + 4 + 2
%e A239667 4 + 4 + 3 + 1 5 + 5 + 4 + 2
%e A239667 5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
%e A239667 4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
%e A239667 3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
%e A239667 3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
%e A239667 1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
%e A239667 4(1) 4(2) 4(3) 4(4) .. 4n
%e A239667 ------------------------------------------------------------------------
%e A239667 1 17 84 262 .. a(n)
%t A239667 CoefficientList[Series[-(9*x^6 + 32*x^5 + 50*x^4 + 58*x^3 + 36*x^2 + 14*x +
%t A239667 1)/((x - 1)^5*(x^2 + x + 1)^2), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Jun 13 2014 *)
%t A239667 LinearRecurrence[{3, -3, 3, -6, 6, -3, 3, -3, 1}, {1, 17, 84, 262, 629, 1289, 2370, 4014, 6393}, 50](* _Vincenzo Librandi_, Aug 29 2015 *)
%t A239667 Table[Total[IntegerPartitions[4 n,{4}][[All,1]]],{n,40}] (* _Harvey P. Dale_, Apr 25 2020 *)
%o A239667 (PARI) Vec(-x*(9*x^6+32*x^5+50*x^4+58*x^3+36*x^2+14*x+1) / ((x-1)^5*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Mar 23 2014
%o A239667 (Magma) I:=[1,17,84,262,629,1289,2370,4014,6393]; [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..45]]; // _Vincenzo Librandi_, Aug 29 2015
%Y A239667 Cf. A238328, A238340, A238702, A238705, A238706, A239056, A239057, A239059, A239186.
%K A239667 nonn,easy
%O A239667 1,2
%A A239667 _Wesley Ivan Hurt_ and _Antonio Osorio_, Mar 23 2014