

A160125


Number of squares and rectangles that are created at the nth stage in the toothpick structure (see A139250).


9



0, 0, 2, 2, 0, 4, 10, 6, 0, 4, 8, 4, 4, 20, 30, 14, 0, 4, 8, 4, 4, 20, 28, 12, 4, 16, 20, 12, 28, 72, 78, 30, 0, 4, 8, 4, 4, 20, 28, 12, 4, 16, 20, 12, 28, 72, 76, 28, 4, 16, 20, 12, 28, 68, 68, 28, 24, 52, 52, 52, 128, 224, 190, 62, 0, 4, 8, 4, 4, 20, 28, 12, 4, 16, 20, 12, 28, 72
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..78.
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.


MAPLE

Maple program from N. J. A. Sloane, Feb 01 2010:
# First construct A168131:
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;
# Then construct A160125:
r := proc(n) option remember; local k, i;
if (n<=2) then RETURN(0)
elif (n <= 4) then RETURN(2)
else
k:=floor(log(n)/log(2)); i:=n2^k;
if (i=0) then RETURN(2^k2)
elif (i<=2^k2) then RETURN(4*w(i));
else RETURN(4*w(i)+2);
fi; fi; end;
[seq(r(n), n=0..200)];


CROSSREFS

First differences of A160124.
Cf. toothpick sequence A139250.
Cf. A159786, A159787, A159788, A159789, A160124, A160126, A160127.
Sequence in context: A009545 A084102 A221609 * A151868 A052079 A291483
Adjacent sequences: A160122 A160123 A160124 * A160126 A160127 A160128


KEYWORD

nonn


AUTHOR

Omar E. Pol, May 03 2009


EXTENSIONS

Terms beyond a(10) from R. J. Mathar, Jan 21 2010


STATUS

approved



