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 A383464 #28 Jun 30 2025 09:27:55
%S A383464 1,4,23,58,109,176,259,358,473,604,751,914,1093,1288,1499,1726,1969,
%T A383464 2228,2503,2794,3101,3424,3763,4118,4489,4876,5279,5698,6133,6584,
%U A383464 7051,7534,8033,8548,9079,9626,10189,10768,11363,11974,12601,13244,13903,14578,15269
%N A383464 a(n) = 8*n^2 - 5*n + 1.
%C A383464 This is equal to A139272(n) + 1, but has its own entry because of an important geometrical interpretation.
%C A383464 Definition: A k-legged Wu is a pencil of k semi-infinite lines originating from a common point.
%C A383464 A 2-legged Wu is a long-legged V (see A130883), and a 3-legged Wu is a long-legged Wu as in A140064.
%C A383464 Theorem (David Cutler, Jonathan Pei, and Edward Xiong, Jun 24 2025): a(n) is the maximum number of regions in the plane that can be formed from n copies of a 4-legged Wu.
%C A383464 Proof: [To be added]
%H A383464 Vincenzo Librandi, <a href="/A383464/b383464.txt">Table of n, a(n) for n = 0..3499</a>
%H A383464 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A383464 G.f.: (1 + x + 14*x^2)/(1 - x)^3.
%F A383464 E.g.f.: exp(x)*(1 + 3*x + 8*x^2). - _Stefano Spezia_, Jun 30 2025
%t A383464 LinearRecurrence[{3,-3,1},{1,4,23},50] (* _Vincenzo Librandi_, Jun 27 2025 *)
%o A383464 (Magma) I:=[1, 4, 23]; [n le 3 select I[n] else 3*Self(n-1)-3* Self(n-2)+Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Jun 27 2025
%Y A383464 Cf. A130083, A139272, A140064.
%K A383464 nonn,easy
%O A383464 0,2
%A A383464 _N. J. A. Sloane_, Jun 26 2025