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

Author

Omar E. Pol, Sep 21 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
		

Links

• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Row sums give A211012.

Cf. A020988, A139250, A160124, A211016, A211018, A211019.

Formula

T(n,k) = A211016(n,k)*2^(k-1).

T(n,1) = 4*A020988(n-2), n>=2.