A211017 T(n,k) = total area of all squares and rectangles of area 2^(k-1) after 2^n stages in the toothpick structure of A139250, n>=1, k>=1, assuming the toothpicks have length 2. Triangle read by rows.

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

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^(k-1).

T(n,1) = 4*A020988(n-2), 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 1 X 1.
T(5,2) = 424 is the total area of all rectangles of size 1 X 2.
T(5,3) = 208 is the total area of all squares of size 2 X 2 and of all rectangles of size 1 X 4.
T(5,4) = 96 is the total area of all rectangles of size 2 X 4.
T(5,5) = 64 is the total area of all rectangles of size 2 X 8.
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