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A245550 a(0)=0; for n >= 1, a(n) = f(n) - 2*f(floor((n-1)/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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n >= 1, a(n) is the number of ON cells in the n-th generation of the 2-D Mitra-Kumar 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 time-manipulated one-dimensional cellular automata." Complex Systems, 16.3 (2006): 191-207. 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((n-1)/2)+f((n+1)/2); fi; end;

g:=n->f(n)-2*f(floor((n-1)/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

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Last modified January 23 22:16 EST 2020. Contains 331177 sequences. (Running on oeis4.)