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 A238702 #61 Jun 19 2024 22:07:47
%S A238702 1,6,21,55,119,227,396,645,996,1474,2106,2922,3955,5240,6815,8721,
%T A238702 11001,13701,16870,20559,24822,29716,35300,41636,48789,56826,65817,
%U A238702 75835,86955,99255,112816,127721,144056,161910,181374,202542,225511,250380,277251,306229
%N A238702 Sum of the smallest parts of the partitions of 4n into 4 parts.
%C A238702 Partial sums of A238340. - _Wesley Ivan Hurt_, May 27 2014
%H A238702 Vincenzo Librandi, <a href="/A238702/b238702.txt">Table of n, a(n) for n = 1..100</a>
%H A238702 Antonio Osorio, <a href="https://mpra.ub.uni-muenchen.de/id/eprint/56690">A Sequential Allocation Problem: The Asymptotic Distribution of Resources</a>, Munich Personal RePEc Archive, 2014.
%H A238702 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A238702 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-5,6,-4,1).
%F A238702 G.f.: -x*(x+1)*(2*x^2+x+1) / ((x-1)^5*(x^2+x+1)). - _Colin Barker_, Mar 10 2014
%F A238702 a(n) = (1/9)*n^4 + (1/3)*n^3 + (5/18)*n^2 + (1/6)*n + O(1). - _Ralf Stephan_, May 29 2014
%F A238702 a(n) = Sum_{i=1..n} A238340(i). - _Wesley Ivan Hurt_, May 29 2014
%F A238702 a(n) = (1/4) * Sum_{i=1..n} A238328(i)/i. - _Wesley Ivan Hurt_, May 29 2014
%F A238702 Recurrence: 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) = b(n)/(4n) + a(n-1), for n>1. - _Wesley Ivan Hurt_, Jun 27 2014
%F A238702 E.g.f.: (exp(x)*(4 + 3*x*(16 + x*(37 + 2*x*(9 + x)))) - 4*exp(-x/2)*cos(sqrt(3)*x/2))/54. - _Stefano Spezia_, Feb 09 2023
%F A238702 a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 5*a(n-4) + 6*a(n-5) - 4*a(n-6) + a(n-7). - _Wesley Ivan Hurt_, Jun 19 2024
%e A238702 Add the numbers in the last column for a(n):
%e A238702 13 + 1 + 1 + 1
%e A238702 12 + 2 + 1 + 1
%e A238702 11 + 3 + 1 + 1
%e A238702 10 + 4 + 1 + 1
%e A238702 9 + 5 + 1 + 1
%e A238702 8 + 6 + 1 + 1
%e A238702 7 + 7 + 1 + 1
%e A238702 11 + 2 + 2 + 1
%e A238702 10 + 3 + 2 + 1
%e A238702 9 + 4 + 2 + 1
%e A238702 8 + 5 + 2 + 1
%e A238702 7 + 6 + 2 + 1
%e A238702 9 + 3 + 3 + 1
%e A238702 8 + 4 + 3 + 1
%e A238702 7 + 5 + 3 + 1
%e A238702 6 + 6 + 3 + 1
%e A238702 7 + 4 + 4 + 1
%e A238702 6 + 5 + 4 + 1
%e A238702 5 + 5 + 5 + 1
%e A238702 9 + 1 + 1 + 1 10 + 2 + 2 + 2
%e A238702 8 + 2 + 1 + 1 9 + 3 + 2 + 2
%e A238702 7 + 3 + 1 + 1 8 + 4 + 2 + 2
%e A238702 6 + 4 + 1 + 1 7 + 5 + 2 + 2
%e A238702 5 + 5 + 1 + 1 6 + 6 + 2 + 2
%e A238702 7 + 2 + 2 + 1 8 + 3 + 3 + 2
%e A238702 6 + 3 + 2 + 1 7 + 4 + 3 + 2
%e A238702 5 + 4 + 2 + 1 6 + 5 + 3 + 2
%e A238702 5 + 3 + 3 + 1 6 + 4 + 4 + 2
%e A238702 4 + 4 + 3 + 1 5 + 5 + 4 + 2
%e A238702 5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
%e A238702 4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
%e A238702 3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
%e A238702 3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
%e A238702 1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
%e A238702 4(1) 4(2) 4(3) 4(4) .. 4n
%e A238702 ------------------------------------------------------------------------
%e A238702 1 6 21 55 .. a(n)
%t A238702 CoefficientList[Series[(x + 1)*(2*x^2 + x + 1)/((1 - x)^5*(x^2 + x + 1)), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Jun 27 2014 *)
%t A238702 LinearRecurrence[{4, -6, 5, -5, 6, -4, 1}, {1, 6, 21, 55, 119, 227, 396}, 50] (* _Vincenzo Librandi_, Aug 29 2015 *)
%o A238702 (PARI) Vec(-x*(x+1)*(2*x^2+x+1)/((x-1)^5*(x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Mar 23 2014
%Y A238702 Cf. A238328, A238340.
%K A238702 nonn,easy
%O A238702 1,2
%A A238702 _Wesley Ivan Hurt_ and _Antonio Osorio_, Mar 03 2014