A077896 Expansion of (1-x)^(-1)/(1+x-2*x^2-2*x^3).

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

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

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 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 (0,3,0,-2).

Crossrefs

Cf. A287468, A287469, A287470.

Programs

Magma

[(1+(-1)^n)*(2^Floor((n+3)/2)-1)/2: n in [0..60]]; // Vincenzo Librandi, May 26 2017

Mathematica

CoefficientList[Series[(1 - x)^(-1) / (1 + x - 2 x^2 - 2 x^3), {x, 0, 60}], x] (* Vincenzo Librandi, May 26 2017 *)

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