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. - Robert Price, May 04 2016
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 linear recurrences with constant coefficients, signature (6,-8).
FORMULA
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)
a(n) = 2*A020522(n+1). - Hussam al-Homsi, Jun 06 2021
E.g.f.: 4*exp(2*x)*(2*exp(2*x) - 1). - Elmo R. Oliveira, Dec 10 2023
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
KEYWORD
easy,nonn
AUTHOR
Jonas Wallgren, Feb 02 2001
EXTENSIONS
Revised by Henry Bottomley, Jun 27 2005
STATUS
approved