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%I #19 Jan 22 2020 20:10:41
%S 1,1,5,1,5,17,85,1,5,17,85,257,1285,4369,21845,1,5,17,85,257,1285,
%T 4369,21845,65537,327685,1114129,5570645,16843009,84215045,286331153,
%U 1431655765,1,5,17,85,257,1285,4369,21845,65537,327685,1114129,5570645
%N A modular binomial sum transform of 2^n.
%C a(2^n) is 1, 5, 5, 5, 5, ... a(2^n+1) is 5, 1, 17, 17, 17, ... a(2(2^n+1)) is 5, 85, 85, 85, ... a(2^n)a(2^n+1) is 5, 5, 85, 85, 85, ...
%C Also, decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 4", based on the 5-celled von Neumann neighborhood. Initialized with a single black (ON) cell at stage zero. - _Robert Price_, Nov 03 2016
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H Robert Price, <a href="/A101692/a101692.tmp.txt">Diagrams of first 20 stages of the cellular automaton</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 <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>
%F a(n) = Sum_{k=0..n} (binomial(2*n+2, k) mod 2)*2^k.
%F a(n) = Sum_{k=0..n} A128937(n, k)*2^(n-k). - _Philippe Deléham_, Oct 09 2007
%Y Cf. A001045, A048896.
%Y Cf. A277916, A277917, A277918.
%K nonn,easy
%O 0,3
%A _Paul Barry_, Dec 11 2004
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