

A245550


a(0)=0; for n >= 1, a(n) = f(n)  2*f(floor((n1)/2)), where f(n) = A006046(n).


1



0, 1, 3, 3, 7, 5, 9, 9, 17, 11, 15, 15, 23, 19, 27, 27, 43, 29, 33, 33, 41, 37, 45, 45, 61, 49, 57, 57, 73, 65, 81, 81, 113, 83, 87, 87, 95, 91, 99, 99, 115, 103, 111, 111, 127, 119, 135, 135, 167, 139, 147, 147, 163, 155, 171, 171, 203, 179, 195, 195, 227, 211, 243, 243, 307, 245, 249, 249, 257
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OFFSET

0,3


COMMENTS

For n >= 1, a(n) is the number of ON cells in the nth generation of the 2D MitraKumar cellular automaton defined as follows. The state of a cell depends on the states of its NW and NE neighbors at the previous generation.
An ON cell remains ON iff 0 or 2 of its neighbors were ON, and an OFF cell turns ON iff exactly one of its neighbors was ON.


REFERENCES

Sugata Mitra and Sujai Kumar. "Fractal replication in timemanipulated onedimensional cellular automata." Complex Systems, 16.3 (2006): 191207. See Fig. 16.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for sequences related to cellular automata


EXAMPLE

The first few generations of the automaton are:
X 0X0 00X00 000X000 0000X0000
X0X 00000 0000000 000000000
X000X 0X000X0 00X000X00
X0X0X0X 000000000
X0000000X
The rows are a subset of the rows of Pascal's triangle A007318 read mod 2 (see A006943). The binary weights of these rows are given by A001316, whose partial sums are A006046, and the formula in the definition follows easily from this.


MAPLE

f:=proc(n) option remember; # A006046
if n <= 1 then n elif n mod 2 = 0 then 3*f(n/2)
else 2*f((n1)/2)+f((n+1)/2); fi; end;
g:=n>f(n)2*f(floor((n1)/2));
[0, seq(g(n), n=1..130)];


PROG

(Haskell)
a245550 n = a245550_list !! n
a245550_list = 0 : zipWith () (tail a006046_list) (h a006046_list)
where h (x:xs) = (2 * x) : (2 * x) : h xs
 Reinhard Zumkeller, Jul 29 2014


CROSSREFS

Cf. A006046, A001316, A006943, A007318.
Sequence in context: A098688 A129266 A129527 * A318461 A085379 A070801
Adjacent sequences: A245547 A245548 A245549 * A245551 A245552 A245553


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jul 29 2014


STATUS

approved



