

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
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: A064644 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



