

A168131


Number of squares and rectangles that are created at the nth stage in the corner toothpick structure (see A152980, A153006).


4



0, 0, 1, 2, 1, 1, 5, 7, 3, 1, 4, 5, 3, 7, 18, 19, 7, 1, 4, 5, 3, 7, 17, 17, 7, 6, 13, 13, 13, 32, 56, 47, 15, 1, 4, 5, 3, 7, 17, 17, 7, 6, 13, 13, 13, 32, 55, 45, 15, 6, 13, 13, 13, 31, 51, 41, 20, 25, 39, 39, 58, 120, 160, 111, 31, 1, 4, 5, 3, 7, 17, 17, 7, 6, 13, 13, 13, 32, 55, 45, 15, 6
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OFFSET

0,4


COMMENTS

Essentially the first differences of A170926.  Omar E. Pol, Feb 16 2013


LINKS

Table of n, a(n) for n=0..81.
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4*3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


FORMULA

See Maple program for recurrence.


EXAMPLE

If written as a triangle:
0,
0,
1,2,
1,1,5,7,
3,1,4,5,3,7,18,19,
7,1,4,5,3,7,17,17,7,6,13,13,13,32,56,47,
15,1,4,5,3,7,17,17,7,6,13,13,13,32,55,45,15,6,13,13,13,31,51,41,20,...
The rows (omitting the first term) converge to A170929.


MAPLE

w := proc(n) option remember; local k, i;
if (n=0) then RETURN(0)
elif (n <= 3) then RETURN(n1)
else
k:=floor(log(n)/log(2));
i:=n2^k;
if (i=0) then RETURN(2^(k1)1)
elif (i<2^k2) then RETURN(2*w(i)+w(i+1));
elif (i=2^k2) then RETURN(2*w(i)+w(i+1)+1);
else RETURN(2*w(i)+w(i+1)+2);
fi;
fi;
end;
[seq(w(n), n=0..256)];


CROSSREFS

Cf. A152980, A153006, A170926, A160124, A160125, A139250.
Sequence in context: A306444 A090210 A248925 * A024462 A049252 A098315
Adjacent sequences: A168128 A168129 A168130 * A168132 A168133 A168134


KEYWORD

nonn


AUTHOR

Omar E. Pol, Jan 18 2010


EXTENSIONS

Edited and extended by N. J. A. Sloane, Feb 01 2010


STATUS

approved



