OFFSET
0,4
COMMENTS
Also, the decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 673", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 23 2017
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Wolfram Research, Wolfram Atlas of Simple Programs
Index entries for linear recurrences with constant coefficients, signature (1, 4, -4).
FORMULA
a(2n+1) = a(2n+2)= A083420(n).
a(n+1)-2a(n) = (-1)^n*A014551(n), n>0.
a(n+1)-2a(n)-1 = 2*(-1)^n*A131577(n).
O.g.f.: x(1+2x^2)/((2x-1)(1+2x)(x-1)). - R. J. Mathar, Aug 02 2008
a(n) = a(n-1)+4*a(n-2)-4*a(n-3), a(0)=0, a(1)=1, a(2)=1, a(3)=7. - Harvey P. Dale, May 28 2012
MATHEMATICA
Join[{0}, LinearRecurrence[{1, 4, -4}, {1, 1, 7}, 30]] (* Harvey P. Dale, May 28 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, Jun 23 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Aug 02 2008
STATUS
approved