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A140252 Inverse binomial transform of A140420. 2


%S 0,1,1,7,7,31,31,127,127,511,511,2047,2047,8191,8191,32767,32767,

%T 131071,131071,524287,524287,2097151,2097151,8388607,8388607,33554431,

%U 33554431,134217727,134217727,536870911,536870911

%N Inverse binomial transform of A140420.

%C 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

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

%H Harvey P. Dale, <a href="/A140252/b140252.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

%H Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 4, -4).

%F a(2n+1) = a(2n+2)= A083420(n).

%F a(n+1)-2a(n) = (-1)^n*A014551(n), n>0.

%F a(n+1)-2a(n)-1 = 2*(-1)^n*A131577(n).

%F O.g.f.: x(1+2x^2)/((2x-1)(1+2x)(x-1)). - _R. J. Mathar_, Aug 02 2008

%F 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

%t Join[{0},LinearRecurrence[{1,4,-4},{1,1,7},30]] (* _Harvey P. Dale_, May 28 2012 *)

%K nonn

%O 0,4

%A _Paul Curtz_, Jun 23 2008

%E Edited and extended by _R. J. Mathar_, Aug 02 2008

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)