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 A238706 #35 Jan 06 2023 19:44:07
%S A238706 0,2,11,36,89,183,335,565,894,1347,1952,2738,3738,4988,6525,8390,
%T A238706 10627,13281,16401,20039,24248,29085,34610,40884,47972,55942,64863,
%U A238706 74808,85853,98075,111555,126377,142626,160391,179764,200838,223710,248480,275249,304122
%N A238706 Sum of the smallest parts of the partitions of 4n into 4 parts with smallest part greater than 1.
%H A238706 Vincenzo Librandi, <a href="/A238706/b238706.txt">Table of n, a(n) for n = 1..1000</a>
%H A238706 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 A238706 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A238706 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-5,6,-4,1).
%F A238706 G.f.: x^2*(x-2)*(x+1)*(2*x^2+x+1) / ((x-1)^5*(x^2+x+1)). - _Colin Barker_, Mar 23 2014
%F A238706 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) for n > 7. - _Wesley Ivan Hurt_, Oct 07 2017
%e A238706 Add the numbers > 1 in the last column for a(n):
%e A238706 13 + 1 + 1 + 1
%e A238706 12 + 2 + 1 + 1
%e A238706 11 + 3 + 1 + 1
%e A238706 10 + 4 + 1 + 1
%e A238706 9 + 5 + 1 + 1
%e A238706 8 + 6 + 1 + 1
%e A238706 7 + 7 + 1 + 1
%e A238706 11 + 2 + 2 + 1
%e A238706 10 + 3 + 2 + 1
%e A238706 9 + 4 + 2 + 1
%e A238706 8 + 5 + 2 + 1
%e A238706 7 + 6 + 2 + 1
%e A238706 9 + 3 + 3 + 1
%e A238706 8 + 4 + 3 + 1
%e A238706 7 + 5 + 3 + 1
%e A238706 6 + 6 + 3 + 1
%e A238706 7 + 4 + 4 + 1
%e A238706 6 + 5 + 4 + 1
%e A238706 5 + 5 + 5 + 1
%e A238706 9 + 1 + 1 + 1 10 + 2 + 2 + 2
%e A238706 8 + 2 + 1 + 1 9 + 3 + 2 + 2
%e A238706 7 + 3 + 1 + 1 8 + 4 + 2 + 2
%e A238706 6 + 4 + 1 + 1 7 + 5 + 2 + 2
%e A238706 5 + 5 + 1 + 1 6 + 6 + 2 + 2
%e A238706 7 + 2 + 2 + 1 8 + 3 + 3 + 2
%e A238706 6 + 3 + 2 + 1 7 + 4 + 3 + 2
%e A238706 5 + 4 + 2 + 1 6 + 5 + 3 + 2
%e A238706 5 + 3 + 3 + 1 6 + 4 + 4 + 2
%e A238706 4 + 4 + 3 + 1 5 + 5 + 4 + 2
%e A238706 5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
%e A238706 4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
%e A238706 3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
%e A238706 3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
%e A238706 1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
%e A238706 4(1) 4(2) 4(3) 4(4) .. 4n
%e A238706 ------------------------------------------------------------------------
%e A238706 0 2 11 36 .. a(n)
%t A238706 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}]; b[n_] := a[n]/(4 n); b[0] = 0; c[1] = 1; c[n_] := b[n] + c[n - 1]; Table[c[n] - (b[n] - b[n - 1]), {n, 50}]
%t A238706 CoefficientList[Series[x (x - 2) (x + 1) (2 x^2 + x + 1)/((x - 1)^5 (x^2 + x + 1)), {x, 0, 40}],x] (* _Vincenzo Librandi_, Mar 24 2014 *)
%t A238706 Table[Total[Select[IntegerPartitions[4n,{4}],#[[-1]]>1&][[All,-1]]],{n,40}] (* or *) LinearRecurrence[{4,-6,5,-5,6,-4,1},{0,2,11,36,89,183,335},40] (* _Harvey P. Dale_, Jan 06 2023 *)
%o A238706 (PARI) concat(0, Vec(x^2*(x-2)*(x+1)*(2*x^2+x+1)/((x-1)^5*(x^2+x+1)) + O(x^100))) \\ _Colin Barker_, Mar 23 2014
%o A238706 (Magma) I:=[0,2,11,36,89,183,335]; [n le 7 select I[n] else 4*Self(n-1)-6*Self(n-2)+5*Self(n-3)-5*Self(n-4)+6*Self(n-5)-4*Self(n-6)+Self(n-7): n in [1..40]]; // _Vincenzo Librandi_, Mar 24 2014
%Y A238706 Cf. A238328, A238340, A238702, A238705.
%K A238706 nonn,easy
%O A238706 1,2
%A A238706 _Wesley Ivan Hurt_ and _Antonio Osorio_, Mar 03 2014