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 A308025 #14 Jul 04 2021 09:34:30
%S A308025 0,0,9,19,55,87,168,234,378,490,715,885,1209,1449,1890,2212,2788,3204,
%T A308025 3933,4455,5355,5995,7084,7854,9150,10062,11583,12649,14413,15645,
%U A308025 17670,19080,21384,22984,25585,27387,30303,32319,35568,37810,41410,43890,47859
%N A308025 a(n) = n*(2*n - 3 - (-1)^n)*(5*n - 2 + (-1)^n)/16.
%C A308025 Consider the rectangular prisms with dimensions s X t X t, where n = s + t and s < t. Then a(n) is the sum of the areas of the squares that rest on a given space diagonal in each of the rectangular prisms.
%C A308025 Sum of the squares of the smaller parts and twice the sum of the squares of the larger parts in the partitions of n into two distinct parts.
%H A308025 Colin Barker, <a href="/A308025/b308025.txt">Table of n, a(n) for n = 1..1000</a>
%H A308025 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A308025 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A308025 a(n) = Sum_{i=1..floor((n-1)/2)} i^2 + 2*(n-i)^2.
%F A308025 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).
%F A308025 G.f.: x^3*(9 + 10*x + 9*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3). - _Colin Barker_, May 17 2019
%t A308025 Table[n*(2 n - 3 - (-1)^n)*(5 n - 2 + (-1)^n)/16, {n, 60}]
%o A308025 (PARI) concat([0,0], Vec(x^3*(9 + 10*x + 9*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3) + O(x^40))) \\ _Colin Barker_, May 17 2019
%Y A308025 Cf. A294286.
%K A308025 nonn,easy
%O A308025 1,3
%A A308025 _Wesley Ivan Hurt_, May 09 2019