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 A002023 a(n) = 6*4^n. 14
 6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184, 1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624, 105553116266496, 422212465065984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Peter M. Chema, Mar 02 2017: (Start) Number of rods (line segments) required to make a Sierpinski tetrahedron of side length 2^n. Also equals the number of balls (vertices) in a Sierpinski tetrahedron of side length 2^n+1 minus the number of balls in a Sierpinski tetrahedron of side length 2^n (the first difference in the tetrix numbers). See formula. (End) Equivalently, the number of edges in the (n+1)-Sierpinski tetrahedron graph. - Eric W. Weisstein, Aug 17 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (4). FORMULA From Philippe Deléham, Nov 23 2008: (Start) a(n) = 4*a(n-1) for n > 0, a(0)=6. G.f.: 6/(1-4*x). (End) a(n) = 3*A004171(n). - R. J. Mathar, Mar 08 2011 From Peter M. Chema, Mar 03 2017: (Start) a(n) = A283070(n+1) - A283070(n). a(n) = A004171(n+1) - A004171(n). (End) E.g.f.: 6*exp(4*x). - G. C. Greubel, Aug 17 2017 MATHEMATICA 6*4^Range[0, 100] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *) Table[6 4^n, {n, 0, 20}] (* Eric W. Weisstein, Aug 17 2017 *) LinearRecurrence[{4}, {6}, 20] (* Eric W. Weisstein, Aug 17 2017 *) CoefficientList[Series[6/(1 - 4 x), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 17 2017 *) PROG (MAGMA) [6*4^n: n in [0..30]]; // Vincenzo Librandi, May 16 2011 (PARI) a(n)=6<<(2*n) \\ Charles R Greathouse IV, Apr 17 2012 CROSSREFS Cf. A283070 (vertex count). Cf. A004171. Sequence in context: A253101 A169759 A164908 * A290911 A037505 A048179 Adjacent sequences:  A002020 A002021 A002022 * A002024 A002025 A002026 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified November 13 17:16 EST 2018. Contains 317149 sequences. (Running on oeis4.)