OFFSET
0,3
COMMENTS
Also, the decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 276", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, May 25 2017
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
LINKS
Vincenzo Librandi, 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 (0,3,0,-2).
FORMULA
G.f.: 1/((1 - x)*(1 + x)*(1 - 2*x^2)). - Bruno Berselli, May 26 2017
a(n) = (1 + (-1)^n)*(2^floor((n + 3)/2) - 1)/2. - Vincenzo Librandi, May 27 2017
MATHEMATICA
CoefficientList[Series[(1 - x)^(-1) / (1 + x - 2 x^2 - 2 x^3), {x, 0, 60}], x] (* Vincenzo Librandi, May 26 2017 *)
PROG
(Magma) [(1+(-1)^n)*(2^Floor((n+3)/2)-1)/2: n in [0..60]]; // Vincenzo Librandi, May 26 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved