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A077896 Expansion of (1-x)^(-1)/(1+x-2*x^2-2*x^3). 6
1, 0, 3, 0, 7, 0, 15, 0, 31, 0, 63, 0, 127, 0, 255, 0, 511, 0, 1023, 0, 2047, 0, 4095, 0, 8191, 0, 16383, 0, 32767, 0, 65535, 0, 131071, 0, 262143, 0, 524287, 0, 1048575, 0, 2097151, 0, 4194303, 0, 8388607, 0, 16777215, 0, 33554431, 0, 67108863, 0, 134217727, 0, 268435455 (list; graph; refs; listen; history; text; internal format)
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
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
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
Sequence in context: A249904 A324875 A266437 * A359061 A238942 A046269
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved

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Last modified April 14 07:58 EDT 2024. Contains 371655 sequences. (Running on oeis4.)