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 A298992 #27 Sep 17 2020 16:49:12
%S A298992 0,0,5,12,35,58,112,160,258,340,495,620,845,1022,1330,1568,1972,2280,
%T A298992 2793,3180,3815,4290,5060,5632,6550,7228,8307,9100,10353,11270,12710,
%U A298992 13760,15400,16592,18445,19788,21867,23370,25688,27360,29930,31780,34615,36652
%N A298992 a(n) = (2*n-3-(-1)^n)*(22*n^2-21*n+5*n*(-1)^n)/96.
%C A298992 Consider the partitions of n into two distinct parts (p,q) where p < q. Then a(n) is the total area of the family of rectangles (and the areas of the squares on their sides) with dimensions p and |q - p|.
%H A298992 Colin Barker, <a href="/A298992/b298992.txt">Table of n, a(n) for n = 1..1000</a>
%H A298992 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A298992 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A298992 a(n) = Sum_{i=1..floor((n-1)/2)} i*(n-2*i) + 2*i^2 + 2*(n-2*i)^2.
%F A298992 From _Colin Barker_, Apr 23 2019: (Start)
%F A298992 G.f.: x^3*(5 + 7*x + 8*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3).
%F A298992 a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7.
%F A298992 (End)
%t A298992 Table[(2 n - 3 - (-1)^n) (22 n^2 - 21 n + 5 n (-1)^n)/96, {n, 50}]
%o A298992 (PARI) concat([0,0], Vec(x^3*(5 + 7*x + 8*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3) + O(x^40))) \\ _Colin Barker_, Apr 23 2019
%Y A298992 Cf. A302647, A302758.
%K A298992 nonn,easy
%O A298992 1,3
%A A298992 _Wesley Ivan Hurt_, Apr 16 2018