A245550 a(0)=0; for n >= 1, a(n) = f(n) - 2*f(floor((n-1)/2)), where f(n) = A006046(n).

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

Offset: 0

Author

N. J. A. Sloane, Jul 29 2014

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A006046, A001316, A006943, A007318.

Programs

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

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)];