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 A239056 #34 Jun 20 2024 20:40:19
%S A239056 4,32,120,304,600,1056,1708,2560,3672,5080,6776,8832,11284,14112,
%T A239056 17400,21184,25432,30240,35644,41600,48216,55528,63480,72192,81700,
%U A239056 91936,103032,115024,127832,141600,156364,172032,188760,206584,225400,245376,266548,288800
%N A239056 Sum of the parts in the partitions of 4n into 4 parts with smallest part = 1.
%C A239056 All terms are multiples of 4.
%H A239056 Vincenzo Librandi, <a href="/A239056/b239056.txt">Table of n, a(n) for n = 1..200</a>
%H A239056 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A239056 <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 A239056 G.f.: 4*x*(2*x^6+10*x^5+16*x^4+22*x^3+15*x^2+6*x+1) / ((x-1)^4*(x^2+x+1)^2). - _Colin Barker_, Mar 10 2014
%F A239056 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 A239056 For a(n) add the parts in the partitions of 4n with smallest part = 1.
%e A239056 13 + 1 + 1 + 1
%e A239056 12 + 2 + 1 + 1
%e A239056 11 + 3 + 1 + 1
%e A239056 10 + 4 + 1 + 1
%e A239056 9 + 5 + 1 + 1
%e A239056 8 + 6 + 1 + 1
%e A239056 7 + 7 + 1 + 1
%e A239056 11 + 2 + 2 + 1
%e A239056 10 + 3 + 2 + 1
%e A239056 9 + 1 + 1 + 1 9 + 4 + 2 + 1
%e A239056 8 + 2 + 1 + 1 8 + 5 + 2 + 1
%e A239056 7 + 3 + 1 + 1 7 + 6 + 2 + 1
%e A239056 6 + 4 + 1 + 1 9 + 3 + 3 + 1
%e A239056 5 + 5 + 1 + 1 8 + 4 + 3 + 1
%e A239056 7 + 2 + 2 + 1 7 + 5 + 3 + 1
%e A239056 5 + 1 + 1 + 1 6 + 3 + 2 + 1 6 + 6 + 3 + 1
%e A239056 4 + 2 + 1 + 1 5 + 4 + 2 + 1 7 + 4 + 4 + 1
%e A239056 3 + 3 + 1 + 1 5 + 3 + 3 + 1 6 + 5 + 4 + 1
%e A239056 1 + 1 + 1 + 1 3 + 2 + 2 + 1 4 + 4 + 3 + 1 5 + 5 + 5 + 1
%e A239056 4(1) 4(2) 4(3) 4(4) .. 4n
%e A239056 ------------------------------------------------------------------------
%e A239056 4 32 120 304 .. a(n)
%t A239056 b[n_] := 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}]; Table[b[n], {n, 50}]
%t A239056 LinearRecurrence[{2,-1,2,-4,2,-1,2,-1},{4,32,120,304,600,1056,1708,2560},40] (* _Harvey P. Dale_, Oct 18 2018 *)
%o A239056 (PARI) Vec(4*x*(2*x^6+10*x^5+16*x^4+22*x^3+15*x^2+6*x+1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 22 2014
%Y A239056 Cf. A238328, A238340, A238702, A238705, A238706.
%K A239056 nonn,easy
%O A239056 1,1
%A A239056 _Wesley Ivan Hurt_, Mar 09 2014