cp's OEIS Frontend

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.

%I A211019 #13 Sep 26 2015 01:17:13
%S A211019 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 A211019 13,3,1,2730,3413,853,213,53,13,3,1,10922,13653,3413,853,213,53,13,3,
%U A211019 1,43690,54613,13653,3413,853,213,53,13,3,1,174762,218453
%N 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.
%C A211019 All internal regions in the toothpick structure are squares and rectangles.
%H A211019 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 A211019 T(n,k) = A211016(n,k)/4.
%F A211019 T(n,1) = A020988(n-2), n>=2.
%e A211019 Triangle begins:
%e A211019 0;
%e A211019 0,         1;
%e A211019 2,         3,     1;
%e A211019 10,       13,     3,    1;
%e A211019 42,       53,    13,    3,   1;
%e A211019 170,     213,    53,   13,   3,   1;
%e A211019 682,     853,   213,   53,  13,   3,  1;
%e A211019 2730,   3413,   853,  213,  53,  13,  3,  1;
%e A211019 10922, 13653,  3413,  853, 213,  53, 13,  3, 1;
%e A211019 43690, 54613, 13653, 3413, 853, 213, 53, 13, 3, 1;
%Y A211019 Row sums give 0 together with A014825.
%Y A211019 Cf. A002450, A020988, A072197, A086462, A139250, A160124, A211016, A211017, A211018.
%K A211019 nonn,tabl
%O A211019 1,4
%A A211019 _Omar E. Pol_, Sep 24 2012