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 A239059 #28 Jun 20 2024 20:53:20
%S A239059 2,9,27,61,108,178,276,395,549,743,966,1236,1558,1917,2335,2817,3344,
%T A239059 3942,4616,5343,6153,7051,8010,9064,10218,11441,12771,14213,15732,
%U A239059 17370,19132,20979,22957,25071,27278,29628,32126,34725,37479,40393,43416,46606,49968
%N A239059 Sum of the two smallest parts from the partitions of 4n into 4 parts with smallest part = 1.
%H A239059 Iain Fox, <a href="/A239059/b239059.txt">Table of n, a(n) for n = 1..10000</a> (first 200 terms from Vincenzo Librandi)
%H A239059 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A239059 <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 A239059 G.f.: -x*(x^2+x+2)*(2*x^4-3*x^3-4*x^2-2*x-1) / ((x-1)^4*(x^2+x+1)^2). - _Colin Barker_, Mar 10 2014
%F A239059 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 20 2024
%e A239059 For a(n) add the smallest two parts in the partitions with smallest part equal to 1.
%e A239059 13 + 1 + 1 + 1
%e A239059 12 + 2 + 1 + 1
%e A239059 11 + 3 + 1 + 1
%e A239059 10 + 4 + 1 + 1
%e A239059 9 + 5 + 1 + 1
%e A239059 8 + 6 + 1 + 1
%e A239059 7 + 7 + 1 + 1
%e A239059 11 + 2 + 2 + 1
%e A239059 10 + 3 + 2 + 1
%e A239059 9 + 4 + 2 + 1
%e A239059 8 + 5 + 2 + 1
%e A239059 7 + 6 + 2 + 1
%e A239059 9 + 3 + 3 + 1
%e A239059 8 + 4 + 3 + 1
%e A239059 7 + 5 + 3 + 1
%e A239059 6 + 6 + 3 + 1
%e A239059 7 + 4 + 4 + 1
%e A239059 6 + 5 + 4 + 1
%e A239059 5 + 5 + 5 + 1
%e A239059 9 + 1 + 1 + 1 10 + 2 + 2 + 2
%e A239059 8 + 2 + 1 + 1 9 + 3 + 2 + 2
%e A239059 7 + 3 + 1 + 1 8 + 4 + 2 + 2
%e A239059 6 + 4 + 1 + 1 7 + 5 + 2 + 2
%e A239059 5 + 5 + 1 + 1 6 + 6 + 2 + 2
%e A239059 7 + 2 + 2 + 1 8 + 3 + 3 + 2
%e A239059 6 + 3 + 2 + 1 7 + 4 + 3 + 2
%e A239059 5 + 4 + 2 + 1 6 + 5 + 3 + 2
%e A239059 5 + 3 + 3 + 1 6 + 4 + 4 + 2
%e A239059 4 + 4 + 3 + 1 5 + 5 + 4 + 2
%e A239059 5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
%e A239059 4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
%e A239059 3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
%e A239059 3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
%e A239059 1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
%e A239059 4(1) 4(2) 4(3) 4(4) .. 4n
%e A239059 ------------------------------------------------------------------------
%e A239059 2 9 27 61 .. a(n)
%t A239059 b[n_] := Sum[((i + 2) (Floor[(4 n - 2 - i)/2] - i)) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[b[n], {n, 50}]
%o A239059 (PARI) Vec(-x*(x^2+x+2)*(2*x^4-3*x^3-4*x^2-2*x-1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 22 2014
%Y A239059 Cf. A238328, A238340, A238702, A238705, A238706, A239056, A239057.
%K A239059 nonn,easy
%O A239059 1,1
%A A239059 _Wesley Ivan Hurt_, Mar 09 2014