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 A064201 #27 Dec 25 2024 12:49:22
%S A064201 0,9,72,189,360,585,864,1197,1584,2025,2520,3069,3672,4329,5040,5805,
%T A064201 6624,7497,8424,9405,10440,11529,12672,13869,15120,16425,17784,19197,
%U A064201 20664,22185,23760,25389,27072,28809,30600,32445,34344,36297,38304,40365,42480,44649
%N A064201 9 times octagonal numbers: a(n) = 9*n*(3*n-2).
%D A064201 L. Berzolari, Allgemeine Theorie der Höheren Ebenen Algebraischen Kurven, Encyclopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Band III_2. Heft 3, Leipzig: B. G. Teubner, 1906. p. 341.
%H A064201 Bruno Berselli, <a href="/A064201/b064201.txt">Table of n, a(n) for n = 0..1000</a>
%H A064201 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A064201 a(n) = 9*(n-2)*(3*n-8), with offset 2.
%F A064201 a(n) = 9*A000567(n). - _Omar E. Pol_, Dec 11 2008
%F A064201 a(n) = a(n-1) + 54*n - 45, with n > 0, a(0)=0. - _Vincenzo Librandi_, Dec 15 2010
%F A064201 G.f.: 9*x*(1+5*x)/(1-x)^3. - _Colin Barker_, Feb 29 2012
%F A064201 From _Elmo R. Oliveira_, Dec 25 2024: (Start)
%F A064201 E.g.f.: 9*exp(x)*x*(1 + 3*x).
%F A064201 a(n) = 3*A152751(n).
%F A064201 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)
%t A064201 9*PolygonalNumber[8,Range[0,40]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3,-3,1},{0,9,72},40] (* _Harvey P. Dale_, Aug 01 2020 *)
%o A064201 (PARI) a(n)=9*n*(3*n-2) \\ _Charles R Greathouse IV_, Jun 16 2017
%Y A064201 Cf. A000567, A152751.
%K A064201 nonn,easy
%O A064201 0,2
%A A064201 Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Sep 22 2001
%E A064201 Better definition, corrected offset and edited from _Omar E. Pol_, Dec 11 2008