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 A013731 #56 Feb 16 2025 08:32:32
%S A013731 4,32,256,2048,16384,131072,1048576,8388608,67108864,536870912,
%T A013731 4294967296,34359738368,274877906944,2199023255552,17592186044416,
%U A013731 140737488355328,1125899906842624,9007199254740992,72057594037927936,576460752303423488,4611686018427387904
%N A013731 a(n) = 2^(3*n+2).
%C A013731 Starting rank of the (j-1)-Washtenaw series for the fixed ratio 2^(-j-1) (see Griess). - J. Taylor (jt_cpp(AT)yahoo.com), Apr 03 2004
%C A013731 1/4 + 1/32 + 1/256 + 1/2048 + ... = 2/7. - _Gary W. Adamson_, Aug 29 2008
%C A013731 Independence number of the (n+1)-Sierpinski carpet graph. - _Eric W. Weisstein_, Sep 06 2017
%C A013731 Clique covering number of the (n+1)-Sierpinski carpet graph. - _Eric W. Weisstein_, Apr 22 2019
%H A013731 Vincenzo Librandi, <a href="/A013731/b013731.txt">Table of n, a(n) for n = 0..200</a>
%H A013731 Robert L. Griess Jr. <a href="http://arXiv.org/abs/math/0403480">Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices</a>, arXiv:math/0403480 [math.GR], Mar 28 2004. See Definition 14.21.
%H A013731 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A013731 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CliqueCoveringNumber.html">Clique Covering Number</a>
%H A013731 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependenceNumber.html">Independence Number</a>
%H A013731 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiCarpetGraph.html">Sierpinski Carpet Graph</a>
%H A013731 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A013731 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (8).
%F A013731 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A013731 a(n) = 8*a(n-1), n > 0; a(0)=4.
%F A013731 G.f.: 4/(1-8x). (End)
%F A013731 a(n) = A198852(n) + 1. - _Michel Marcus_, Aug 23 2013
%F A013731 a(n) = A092811(n+1). - _Eric W. Weisstein_, Sep 06 2017
%F A013731 a(n) = 4*A001018(n). - _R. J. Mathar_, May 21 2024
%F A013731 E.g.f.: 4*exp(8*x). - _Stefano Spezia_, May 29 2024
%p A013731 seq(2^(3*n+2),n=0..19); # _Nathaniel Johnston_, Jun 26 2011
%t A013731 (* Start from _Eric W. Weisstein_, Sep 06 2017 *)
%t A013731 Table[2^(3 n + 2), {n, 0, 20}]
%t A013731 2^(3 Range[0, 20] + 2)
%t A013731 LinearRecurrence[{8}, {4}, 20]
%t A013731 CoefficientList[Series[-(4/(-1 + 8 x)), {x, 0, 20}], x]
%t A013731 (* End *)
%o A013731 (Sage) [lucas_number1(3*n, 2, 0) for n in range(1, 20)] # _Zerinvary Lajos_, Oct 27 2009
%o A013731 (Magma) [2^(3*n+2): n in [0..20]]; // _Vincenzo Librandi_, Jun 26 2011
%o A013731 (PARI) a(n)=4<<(3*n) \\ _Charles R Greathouse IV_, Apr 07 2012
%Y A013731 Cf. A001018, A013730, A198852.
%Y A013731 Cf. A092811 (same sequence with 1 prepended).
%K A013731 nonn,easy
%O A013731 0,1
%A A013731 _N. J. A. Sloane_