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A059153 a(n) = 2^(n+2)*(2^(n+1)-1). 7
4, 24, 112, 480, 1984, 8064, 32512, 130560, 523264, 2095104, 8384512, 33546240, 134201344, 536838144, 2147418112, 8589803520, 34359476224, 137438429184, 549754765312, 2199021158400, 8796088827904, 35184363700224, 140737471578112, 562949919866880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A hierarchical sequence (S(W'2{2}c) - see A059126).

a(n) written in base 2: 100, 11000, 1110000, ..., i.e., (n+1) times 1 and (n+2) times 0 (see A163663). - Jaroslav Krizek, Aug 12 2009

Also, the number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 513", based on the 5-celled von Neumann neighborhood.

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..200

J. Wallgren, Hierarchical sequences

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (6,-8).

FORMULA

a(n) = A173787(2*n+3,n+2) = 4*A006516(n+1). (cf. A020522). - Reinhard Zumkeller, Feb 28 2010

From Colin Barker, Apr 28 2013: (Start)

a(n) = 6*a(n-1)-8*a(n-2).

G.f.: 4 / ((2*x-1)*(4*x-1)). (End)

MATHEMATICA

Table[2^(n + 2)*(2^(n + 1) - 1), {n, 0, 23}] (* and *) LinearRecurrence[{6, -8}, {4, 24}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)

PROG

(PARI) { for (n = 0, 200, write("b059153.txt", n, " ", 2^(n + 2)*(2^(n + 1) - 1)); ) } \\ Harry J. Smith, Jun 25 2009

CROSSREFS

Equals A045687(2n+4), A272702.

Sequence in context: A145655 A265975 A306610 * A129032 A270686 A272253

Adjacent sequences:  A059150 A059151 A059152 * A059154 A059155 A059156

KEYWORD

easy,nonn

AUTHOR

Jonas Wallgren, Feb 02 2001

EXTENSIONS

Revised by Henry Bottomley, Jun 27 2005

STATUS

approved

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Last modified October 20 17:41 EDT 2019. Contains 328268 sequences. (Running on oeis4.)