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%I #13 Sep 26 2015 01:17:13
%S 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,
%T 13,3,1,2730,3413,853,213,53,13,3,1,10922,13653,3413,853,213,53,13,3,
%U 1,43690,54613,13653,3413,853,213,53,13,3,1,174762,218453
%N 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.
%C All internal regions in the toothpick structure are squares and rectangles.
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%F T(n,k) = A211016(n,k)/4.
%F T(n,1) = A020988(n-2), n>=2.
%e Triangle begins:
%e 0;
%e 0, 1;
%e 2, 3, 1;
%e 10, 13, 3, 1;
%e 42, 53, 13, 3, 1;
%e 170, 213, 53, 13, 3, 1;
%e 682, 853, 213, 53, 13, 3, 1;
%e 2730, 3413, 853, 213, 53, 13, 3, 1;
%e 10922, 13653, 3413, 853, 213, 53, 13, 3, 1;
%e 43690, 54613, 13653, 3413, 853, 213, 53, 13, 3, 1;
%Y Row sums give 0 together with A014825.
%Y Cf. A002450, A020988, A072197, A086462, A139250, A160124, A211016, A211017, A211018.
%K nonn,tabl
%O 1,4
%A _Omar E. Pol_, Sep 24 2012
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