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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

N. J. A. Sloane

STATUS

approved

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Last modified November 20 00:42 EST 2017. Contains 294957 sequences.