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A168131 Number of squares and rectangles that are created at the n-th 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 (list; graph; refs; listen; history; text; internal format)
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), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-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(n-1)

else

k:=floor(log(n)/log(2));

i:=n-2^k;

if (i=0) then RETURN(2^(k-1)-1)

elif (i<2^k-2) then RETURN(2*w(i)+w(i+1));

elif (i=2^k-2) 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

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)