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 A350043 #21 Jan 28 2024 18:10:18
%S A350043 0,2,7,15,24,36,58,75,104,138,175,217,277,328,399,477,560,650,766,869,
%T A350043 1000,1140,1287,1443,1633,1806,2015,2235,2464,2704,2986,3247,3552,
%U A350043 3870,4199,4541,4933,5300,5719,6153,6600,7062,7582,8073,8624,9192,9775,10375,11041,11674
%N A350043 Sum of all the parts > 1 in the partitions of n into 3 positive integer parts.
%H A350043 Winston de Greef, <a href="/A350043/b350043.txt">Table of n, a(n) for n = 3..10000</a>
%H A350043 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A350043 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-4,-1,2,2,0,-1).
%F A350043 For n >= 4, a(n) = -1 - floor((n-1)/2) + n * Sum_{k=1..floor(n/3)} floor((n-3*k+2)/2).
%F A350043 G.f.: -x^4 * (x^9-x^8-3*x^7+5*x^5+6*x^4-6*x^3-11*x^2-7*x-2) / ((x+1)^2 *(x^2+x+1)^2 *(x-1)^4). - _Alois P. Heinz_, Dec 13 2021
%F A350043 a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10). - _Wesley Ivan Hurt_, Dec 17 2021
%e A350043 a(7) = 24; The partitions of 7 into 3 positive integer parts are (1,1,5), (1,2,4), (1,3,3) and (2,2,3). The sum of all the parts > 1 is then 5+2+4+3+3+2+2+3 = 24.
%t A350043 CoefficientList[Series[-x*(x^9 - x^8 - 3*x^7 + 5*x^5 + 6*x^4 - 6*x^3 - 11*x^2 - 7*x - 2)/((x + 1)^2*(x^2 + x + 1)^2*(x - 1)^4), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Nov 12 2022 *)
%o A350043 (PARI) a(n)=if(n==3, 0, -1 - floor((n-1)/2) + n * sum(k=1,floor(n/3), floor((n-3*k+2)/2))) \\ _Winston de Greef_, Jan 28 2024
%Y A350043 Cf. A069905, A350042.
%K A350043 nonn,easy
%O A350043 3,2
%A A350043 _Wesley Ivan Hurt_, Dec 10 2021