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 A258597 #22 Feb 16 2025 08:33:25
%S A258597 13,39,117,351,1053,3159,9477,28431,85293,255879,767637,2302911,
%T A258597 6908733,20726199,62178597,186535791,559607373,1678822119,5036466357,
%U A258597 15109399071,45328197213,135984591639,407953774917,1223861324751,3671583974253,11014751922759
%N A258597 a(n) = 13*3^n.
%C A258597 Also maximum leaf number of the (n+3)-Apollonian network for n >= 0. - _Eric W. Weisstein_, Jan 17 2018
%H A258597 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ApollonianNetwork.html">Apollonian Network</a>
%H A258597 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumLeafNumber.html">Maximum Leaf Number</a>
%H A258597 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (3).
%F A258597 G.f.: 13/(1-3*x).
%F A258597 a(n) = 3*a(n-1).
%F A258597 a(n) = 13*A000244(n).
%F A258597 E.g.f.: 13*exp(3*x). - _Elmo R. Oliveira_, Aug 16 2024
%t A258597 Table[13 3^n, {n, 0, 30}]
%t A258597 13 3^Range[0, 20] (* _Eric W. Weisstein_, Jan 17 2018 *)
%t A258597 LinearRecurrence[{3}, {13}, 20] (* _Eric W. Weisstein_, Jan 17 2018 *)
%t A258597 CoefficientList[Series[13/(1 - 3 x), {x, 0, 20}], x] (* _Eric W. Weisstein_, Jan 17 2018 *)
%o A258597 (Magma) [13*3^n: n in [0..30]];
%Y A258597 Cf. k*3^n: A000244 (k=1,3,9), A008776 (k=2,6), A003946 (k=4), A005030 (k=5), A005032 (k=7), A005051 (k=8), A005052 (k=10), A120354 (k=11), A003946 (k=12), this sequence (k=13), A258598 (k=17), A176413 (k=19).
%K A258597 nonn,easy
%O A258597 0,1
%A A258597 _Vincenzo Librandi_, Jun 05 2015