A211008 Triangle read by rows: T(n,k) = number of squares and rectangles of area 2^(k-1) after n-th stage in the toothpick structure of A139250, n>=1, k>=1, assuming the toothpicks have length 2.

0, 0, 0, 2, 0, 4, 0, 4, 4, 4, 8, 8, 2, 8, 12, 4, 8, 12, 4, 12, 12, 4, 16, 16, 4, 16, 20, 4, 20, 20, 4, 32, 28, 4, 40, 44, 8, 2, 40, 52, 12, 4, 40, 52, 12, 4, 44, 52, 12, 4, 48, 56, 12, 4, 48, 60, 12, 4, 52, 60, 12, 4, 64, 68, 12, 4, 72, 84, 16, 4

Offset: 1

Author

Omar E. Pol, Sep 18 2012

Keywords

• nonn
• tabf

Comments

It appears that the number of rectangles of area 2 in the toothpick structure of A139250 equals the number of hearts in the Q-toothpick cellular automaton of A187210. See conjecture in formula section.

Examples

			For n = 8 in the toothpick structure after 8 stages we have that:
T(8,1) = 8 is the number of squares of size 1 X 1.
T(8,2) = 12 is the number of rectangles of size 1 X 2.
T(8,3) = 4 is the number of squares of size 2 X 2.
Written as an irregular array the sequence begins:
   0;
   0;
   0,  2;
   0,  4;
   0,  4;
   4,  4;
   8,  8,  2;
   8, 12,  4;
   8, 12,  4;
  12, 12,  4;
  16, 16,  4;
  16, 20,  4;
  20, 20,  4;
  32, 28,  4;
  40, 44,  8,  2;
  40, 52, 12,  4;
		

Links

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

Crossrefs

Zero together with the row sums gives A160124.

Cf. A139250, A159786, A160125, A168131, A187210, A188346, A211016, A211017, A211019.

Formula

It appears that T(n,2) = A188346(n+2) (checked by hand up to n = 128 in the toothpick structure of A139250).