A211019 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, divided by 4, n>=1, k>=1, assuming the toothpicks have length 2.

0, 0, 1, 2, 3, 1, 10, 13, 3, 1, 42, 53, 13, 3, 1, 170, 213, 53, 13, 3, 1, 682, 853, 213, 53, 13, 3, 1, 2730, 3413, 853, 213, 53, 13, 3, 1, 10922, 13653, 3413, 853, 213, 53, 13, 3, 1, 43690, 54613, 13653, 3413, 853, 213, 53, 13, 3, 1, 174762, 218453

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..57.

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

Formula

T(n,k) = A211016(n,k)/4.

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

Example

Triangle begins:
0;
0,         1;
2,         3,     1;
10,       13,     3,    1;
42,       53,    13,    3,   1;
170,     213,    53,   13,   3,   1;
682,     853,   213,   53,  13,   3,  1;
2730,   3413,   853,  213,  53,  13,  3,  1;
10922, 13653,  3413,  853, 213,  53, 13,  3, 1;
43690, 54613, 13653, 3413, 853, 213, 53, 13, 3, 1;

Crossrefs

Row sums give 0 together with A014825.

Cf. A002450, A020988, A072197, A086462, A139250, A160124, A211016, A211017, A211018.

Sequence in context: A247563 A322702 A107855 * A298401 A009026 A046222

Adjacent sequences: A211016 A211017 A211018 * A211020 A211021 A211022

Keyword

nonn,tabl

Author

Omar E. Pol, Sep 24 2012

Status

approved