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 A386851 #14 Aug 15 2025 14:04:36
%S A386851 0,3,7,13,20,30,40,53,67,83,100,120,140,163,187,213,240,270,300,333,
%T A386851 367,403,440,480,520,563,607,653,700,750,800,853,907,963,1020,1080,
%U A386851 1140,1203,1267,1333,1400,1470,1540,1613,1687,1763,1840,1920,2000,2083,2167,2253
%N A386851 a(n) = floor(5*n^2/6).
%H A386851 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
%F A386851 a(n) = A227347(n)-A227347(n-1) for n>1.
%F A386851 a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6) for n > 6.
%F A386851 a(2n) = A330451(n).
%F A386851 G.f.: -x^2*(3*x^2 + 4*x + 3)/((x - 1)^3*(x + 1)*(x^2 + x + 1)).
%t A386851 a[n_]:=Floor[5n^2/6];Array[a,52] (* or *) Rest[CoefficientList[Series[-x^2*(3*x^2 + 4*x + 3)/((x - 1)^3*(x + 1)*(x^2 + x + 1)),{x,0,52}],x]] (* or *) LinearRecurrence[{1,1,0,-1,-1,1},{0, 3, 7, 13, 20, 30, 40},52] (* _James C. McMahon_, Aug 12 2025 *)
%o A386851 (Python)
%o A386851 def A386851(n): return 5*n**2//6
%Y A386851 Cf. A227347 (partial sums), A330451.
%K A386851 nonn,easy
%O A386851 1,2
%A A386851 _Chai Wah Wu_, Aug 05 2025