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

1,4

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.

Links

Table of n, a(n) for n=1..70.

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

Formula

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

Example

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;

Crossrefs

Zero together with the row sums gives A160124.

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

Sequence in context: A082024 A337599 A322337 * A365344 A366543 A286663

Adjacent sequences: A211005 A211006 A211007 * A211009 A211010 A211011

Keyword

nonn,tabf

Author

Omar E. Pol, Sep 18 2012

Status

approved