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 A386485 #18 Sep 04 2025 14:56:27
%S A386485 1,2,12,32,62,102,152,212,282,362,452,552,662,782,912,1052,1202,1362,
%T A386485 1532,1712,1902,2102,2312,2532,2762,3002,3252,3512,3782,4062,4352,
%U A386485 4652,4962,5282,5612,5952,6302,6662,7032,7412,7802,8202,8612,9032,9462,9902,10352,10812,11282,11762,12252,12752,13262,13782,14312
%N A386485 a(0) = 1; thereafter a(n) = 5*n^2 - 5*n + 2.
%C A386485 Maximum number of regions that can be formed in the plane by drawing n regular pentagons (of any size). Differs from A062786 and A124080 by a small constant shift, but is included here because of its geometrical applications.
%H A386485 Paolo Xausa, <a href="/A386485/b386485.txt">Table of n, a(n) for n = 0..10000</a>
%H A386485 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A386485 G.f.: -(x^3+9*x^2-x+1)/(x-1)^3.
%F A386485 From _Elmo R. Oliveira_, Sep 04 2025: (Start)
%F A386485 E.g.f.: exp(x)*(2 + 5*x^2) - 1.
%F A386485 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%t A386485 A386485[n_] := If[n == 0, 1, 5*n*(n - 1) + 2]; Array[A386485, 60, 0] (* or *)
%t A386485 LinearRecurrence[{3, -3, 1}, {1, 2, 12, 32}, 60] (* _Paolo Xausa_, Aug 18 2025 *)
%Y A386485 Cf. A051890, A069894, A077588, A386480.
%Y A386485 See also A062786, A124080.
%K A386485 nonn,easy,changed
%O A386485 0,2
%A A386485 _N. J. A. Sloane_, Aug 18 2025