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 A380353 #26 Feb 09 2025 18:09:57
%S A380353 1,12,64,217,561,1216,2332,4089,6697,10396,15456,22177,30889,41952,
%T A380353 55756,72721,93297,117964,147232,181641,221761,268192,321564,382537,
%U A380353 451801,530076,618112,716689,826617,948736,1083916,1233057,1397089,1576972,1773696,1988281,2221777
%N A380353 a(n) = (n^2 - n + 2) * (5*n^2 - 5*n + 2) / 4.
%C A380353 First differences of A072474 (sum of next n squares).
%H A380353 Kelvin Voskuijl, <a href="/A380353/b380353.txt">Table of n, a(n) for n = 1..10000</a>
%H A380353 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A380353 a(n) = A051624(A000124(n-1)).
%F A380353 G.f.: x*(1+3*x+x^2)*(1+4*x+x^2)/(1-x)^5. - _Jinyuan Wang_, Jan 23 2025
%F A380353 E.g.f.: exp(x)*(4 + 22*x^2 + 20*x^3 + 5*x^4)/4 - 1. - _Stefano Spezia_, Jan 28 2025
%t A380353 Table[((n^2 - n + 2)*(5*n^2 - 5*n + 2))/4, {n, 1, 40}]
%o A380353 (PARI) a(n) = (n^2 - n + 2) * (5*n^2 - 5*n + 2) / 4
%Y A380353 Cf. A072474 (partial sums), A051624, A000124.
%Y A380353 Cf. A005448 (first difference of sum of next n natural numbers).
%K A380353 nonn,easy
%O A380353 1,2
%A A380353 _Kelvin Voskuijl_, Jan 22 2025