A211016 Triangle read by rows: T(n,k) = number of 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.

0, 0, 4, 8, 12, 4, 40, 52, 12, 4, 168, 212, 52, 12, 4, 680, 852, 212, 52, 12, 4, 2728, 3412, 852, 212, 52, 12, 4, 10920, 13652, 3412, 852, 212, 52, 12, 4, 43688, 54612, 13652, 3412, 852, 212, 52, 12, 4, 174760, 218452, 54612, 13652, 3412, 852, 212, 52, 12, 4

Offset: 1

Author

Omar E. Pol, Sep 18 2012

Keywords

• nonn
• tabl

Comments

All internal regions in the toothpick structure are squares and rectangles.

Examples

			For n = 5 in the toothpick structure after 2^5 stages we have that:
T(5,1) = 168 is the number of squares of size 1 X 1.
T(5,2) = 212 is the number of rectangles of size 1 X 2.
T(5,3) = 52 is the total number of squares of size 2 X 2 and of rectangles of size 1 X 4.
T(5,4) = 12 is the number of rectangles of size 2 X 4.
T(5,5) = 4 is the number of rectangles of size 2 X 8.
Triangle begins:
       0;
       0,      4;
       8,     12,     4;
      40,     52,    12,     4;
     168,    212,    52,    12,    4;
     680,    852,   212,    52,   12,   4;
    2728,   3412,   852,   212,   52,  12,   4;
   10920,  13652,  3412,   852,  212,  52,  12,  4;
   43688,  54612, 13652,  3412,  852, 212,  52, 12,  4;
  174760, 218452, 54612, 13652, 3412, 852, 212, 52, 12, 4;
		

Links

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

Crossrefs

Row sums give 0 together with A145655.

Cf. A020988, A072197, A080675, A139250, A160124, A211008, A211017, A211018, A211019.

Formula

T(n,k) = A211008(2^n,k) = 4*A211019(n,k).

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