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 A013731 a(n) = 2^(3*n+2). 8
 4, 32, 256, 2048, 16384, 131072, 1048576, 8388608, 67108864, 536870912, 4294967296, 34359738368, 274877906944, 2199023255552, 17592186044416, 140737488355328, 1125899906842624, 9007199254740992, 72057594037927936, 576460752303423488 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 1/4 + 1/32 + 1/256 + 1/2048 + ... = 2/7. - Gary W. Adamson, Aug 29 2008 Independence number of the (n+1)-Sierpinski carpet graph. - Eric W. Weisstein, Sep 06 2017 Clique covering number of the (n+1)-Sierpinski carpet graph. - Eric W. Weisstein, Apr 22 2019 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Robert L. Griess Jr. Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices, arXiv:math/0403480 [math.GR], Mar 28 2004. See Definition 14.21. Tanya Khovanova, Recursive Sequences Eric Weisstein's World of Mathematics, Clique Covering Number Eric Weisstein's World of Mathematics, Independence Number Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph Index entries for linear recurrences with constant coefficients, signature (8). FORMULA From Philippe Deléham, Nov 23 2008: (Start) a(n) = 8*a(n-1), n > 0; a(0)=4. G.f.: 4/(1-8x). (End) a(n) = A198852(n) + 1. - Michel Marcus, Aug 23 2013 a(n) = A092811(n+1). - Eric W. Weisstein, Sep 06 2017 MAPLE seq(2^(3*n+2), n=0..19); # Nathaniel Johnston, Jun 26 2011 MATHEMATICA (* Start from Eric W. Weisstein, Sep 06 2017 *) Table[2^(3 n + 2), {n, 0, 20}] 2^(3 Range[0, 20] + 2) LinearRecurrence[{8}, {4}, 20] CoefficientList[Series[-(4/(-1 + 8 x)), {x, 0, 20}], x] (* End *) PROG (Sage) [lucas_number1(3*n, 2, 0) for n in range(1, 20)] # Zerinvary Lajos, Oct 27 2009 (MAGMA) [2^(3*n+2): n in [0..20]]; // Vincenzo Librandi, Jun 26 2011 (PARI) a(n)=4<<(3*n) \\ Charles R Greathouse IV, Apr 07 2012 CROSSREFS Cf. A013730. Cf. A092811 (same sequence with 1 prepended). Sequence in context: A317512 A300177 A092811 * A009509 A036725 A065089 Adjacent sequences:  A013728 A013729 A013730 * A013732 A013733 A013734 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 20 16:51 EDT 2020. Contains 337905 sequences. (Running on oeis4.)