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 A239057 #22 Jun 22 2024 09:58:35
%S A239057 3,28,110,285,570,1012,1647,2480,3570,4953,6622,8648,11067,13860,
%T A239057 17110,20853,25058,29820,35175,41080,47642,54897,62790,71440,80883,
%U A239057 91052,102078,113997,126730,140420,155103,170688,187330,205065,223790,243672,264747,286900
%N A239057 Sum of the parts in the partitions of 4n into 4 parts with smallest part equal to 1 minus the number of these partitions.
%H A239057 Vincenzo Librandi, <a href="/A239057/b239057.txt">Table of n, a(n) for n = 1..1000</a>
%H A239057 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A239057 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-4,2,-1,2,-1).
%F A239057 a(n) = A239056(n) - A238705(n).
%F A239057 G.f.: x*(2*x^2+x+3)*(5*x^4+19*x^3+16*x^2+7*x+1)/((x^2+x+1)^2*(x-1)^4). - _Alois P. Heinz_, Mar 11 2014
%F A239057 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) - a(n-6) + 2*a(n-7) - a(n-8). - _Wesley Ivan Hurt_, Jun 22 2024
%e A239057 For a(n) add the numbers in the first 3 columns.
%e A239057 13 + 1 + 1 + 1
%e A239057 12 + 2 + 1 + 1
%e A239057 11 + 3 + 1 + 1
%e A239057 10 + 4 + 1 + 1
%e A239057 9 + 5 + 1 + 1
%e A239057 8 + 6 + 1 + 1
%e A239057 7 + 7 + 1 + 1
%e A239057 11 + 2 + 2 + 1
%e A239057 10 + 3 + 2 + 1
%e A239057 9 + 1 + 1 + 1 9 + 4 + 2 + 1
%e A239057 8 + 2 + 1 + 1 8 + 5 + 2 + 1
%e A239057 7 + 3 + 1 + 1 7 + 6 + 2 + 1
%e A239057 6 + 4 + 1 + 1 9 + 3 + 3 + 1
%e A239057 5 + 5 + 1 + 1 8 + 4 + 3 + 1
%e A239057 7 + 2 + 2 + 1 7 + 5 + 3 + 1
%e A239057 5 + 1 + 1 + 1 6 + 3 + 2 + 1 6 + 6 + 3 + 1
%e A239057 4 + 2 + 1 + 1 5 + 4 + 2 + 1 7 + 4 + 4 + 1
%e A239057 3 + 3 + 1 + 1 5 + 3 + 3 + 1 6 + 5 + 4 + 1
%e A239057 1 + 1 + 1 + 1 3 + 2 + 2 + 1 4 + 4 + 3 + 1 5 + 5 + 5 + 1
%e A239057 4(1) 4(2) 4(3) 4(4) .. 4n
%e A239057 ------------------------------------------------------------------------
%e A239057 3 28 110 285 .. a(n)
%t A239057 b[n_] := (4 n - 1) Sum[((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i) + (i + 2) (Floor[(4 n - 2 - i)/2] - i)) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]/(4 n); Table[b[n], {n, 50}]
%t A239057 CoefficientList[Series[(2 x^2 + x + 3) (5 x^4 + 19 x^3 + 16 x^2 + 7 x + 1)/((x^2 + x + 1)^2 (x - 1)^4), {x, 0, 50}], x] (* _Vincenzo Librandi_, Mar 13 2014 *)
%Y A239057 Cf. A238328, A238340, A238702, A238705, A238706, A239056.
%K A239057 nonn
%O A239057 1,1
%A A239057 _Wesley Ivan Hurt_, Mar 09 2014