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 A144312 #24 May 10 2025 03:11:12
%S A144312 0,15,55,120,210,325,465,630,820,1035,1275,1540,1830,2145,2485,2850,
%T A144312 3240,3655,4095,4560,5050,5565,6105,6670,7260,7875,8515,9180,9870,
%U A144312 10585,11325,12090,12880,13695,14535,15400,16290,17205,18145,19110,20100
%N A144312 a(n) = 5*n*(5*n + 1)/2.
%H A144312 Stefano Spezia, <a href="/A144312/b144312.txt">Table of n, a(n) for n = 0..10000</a>
%H A144312 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A144312 a(n) = A000217(5*n).
%F A144312 a(n) = a(n-1) + 25*n - 10 (with a(0) = 0). - _Vincenzo Librandi_, Nov 25 2010
%F A144312 From _Stefano Spezia_, Jun 12 2021: (Start)
%F A144312 O.g.f.: 5*x*(3 + 2*x)/(1 - x)^3.
%F A144312 E.g.f.: 5*exp(x)*x*(6 + 5*x)/2.
%F A144312 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%F A144312 From _Amiram Eldar_, May 10 2025: (Start)
%F A144312 Sum_{n>=1} 1/a(n) = 2 - log(5)/2 - sqrt(1+2/sqrt(5))*Pi/5 - log(phi)/sqrt(5), where phi is the golden ratio (A001622).
%F A144312 Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/5 + sqrt(2+2/sqrt(5))*Pi/5 + 2*log(phi)/sqrt(5) - 2. (End)
%t A144312 a[n_] := 5*n*(5*n+1)/2; Array[a, 50, 0] (* _Amiram Eldar_, May 10 2025 *)
%o A144312 (PARI) a(n)=5*n*(5*n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A144312 Cf. A000217, A001622, A014105, A033585, A081266.
%K A144312 nonn,easy
%O A144312 0,2
%A A144312 _Reinhard Zumkeller_, Sep 17 2008