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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 (list; graph; refs; listen; history; text; internal format)
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 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

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 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

FORMULA

a(n) = Sum_{k=0..n} mod(binomial(2*n+2, k), 2)*2^k

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

CROSSREFS

Cf. A001045, A048896.

Cf. A277916, A277917, A277918.

Sequence in context: A143384 A046611 A145825 * A281105 A105060 A229096

Adjacent sequences:  A101689 A101690 A101691 * A101693 A101694 A101695

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Dec 11 2004

STATUS

approved

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)