

A101692


A modular binomial sum transform of 2^n.


3



1, 1, 5, 1, 5, 17, 85, 1, 5, 17, 85, 257, 1285, 4369, 21845, 1, 5, 17, 85, 257, 1285, 4369, 21845, 65537, 327685, 1114129, 5570645, 16843009, 84215045, 286331153, 1431655765, 1, 5, 17, 85, 257, 1285, 4369, 21845, 65537, 327685, 1114129, 5570645
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OFFSET

0,3


COMMENTS

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, ...
Also, decimal representation of the xaxis, from the origin to the right edge, of the nth stage of growth of the twodimensional cellular automaton defined by "Rule 4", based on the 5celled von Neumann neighborhood. Initialized with a single black (ON) cell at stage zero.  Robert Price, Nov 03 2016


REFERENCES

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


LINKS

Table of n, a(n) for n=0..42.
Robert Price, Diagrams of first 20 stages of the cellular automaton
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
Index entries for sequences related to cellular automata
Index to 2D 5Neighbor Cellular Automata
Index to Elementary Cellular Automata


FORMULA

a(n) = Sum_{k=0..n} (binomial(2*n+2, k) mod 2)*2^k.
a(n) = Sum_{k=0..n} A128937(n, k)*2^(nk).  Philippe Deléham, Oct 09 2007


CROSSREFS

Cf. A001045, A048896.
Cf. A277916, A277917, A277918.
Sequence in context: A143384 A046611 A145825 * A281105 A327283 A105060
Adjacent sequences: A101689 A101690 A101691 * A101693 A101694 A101695


KEYWORD

nonn,easy


AUTHOR

Paul Barry, Dec 11 2004


STATUS

approved



