

A211017


Triangle read by rows: T(n,k) = total area of all squares and rectangles of area 2^(k1) after 2^n stages in the toothpick structure of A139250, n>=1, k>=1, assuming the toothpicks have length 2.


5



0, 0, 8, 8, 24, 16, 40, 104, 48, 32, 168, 424, 208, 96, 64, 680, 1704, 848, 416, 192, 128, 2728, 6824, 3408, 1696, 832, 384, 256, 10920, 27304, 13648, 6816, 3392, 1664, 768, 512, 43688, 109924, 54608, 27296, 13632, 6784, 3328, 1536, 1024
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OFFSET

1,3


COMMENTS

All internal regions in the toothpick structure are squares and rectangles. The area of every internal region is a power of 2.


LINKS

Table of n, a(n) for n=1..45.
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


FORMULA

T(n,k) = A211016(n,k)*2^(k1).
T(n,1) = 4*A020988(n2), n>=2.


EXAMPLE

For n = 5 in the toothpick structure after 2^5 stages we have that:
T(5,1) = 168 is the total area of all squares of size 1X1.
T(5,2) = 424 is the total area of all rectangles of size 1X2.
T(5,3) = 208 is the total area of all squares of size 2X2 and of all rectangles of size 1X4.
T(5,4) = 96 is the total area of all rectangles of size 2X4.
T(5,5) = 64 is the total area of all rectangles of size 2X8.
Triangle begins:
0;
0, 8;
8, 24, 16;
40, 104, 48, 32;
168, 424, 208, 96, 64;
680, 1704, 848, 416, 192, 128;
2728, 6824, 3408, 1696, 832, 384, 256;
10920, 27304, 13648, 6816, 3392, 1664, 768, 512;


CROSSREFS

Row sums give A211012.
Cf. A020988, A139250, A160124, A211016, A211018, A211019.
Sequence in context: A205382 A109049 A160239 * A037018 A246310 A318542
Adjacent sequences: A211014 A211015 A211016 * A211018 A211019 A211020


KEYWORD

nonn,tabl


AUTHOR

Omar E. Pol, Sep 21 2012


STATUS

approved



