cp's OEIS Frontend

A211017 T(n,k) = total area of all squares and rectangles of area 2^(k-1) after 2^n stages in the toothpick structure of A139250, n>=1, k>=1, assuming the toothpicks have length 2. Triangle read by rows.

%I A211017 #19 Dec 24 2022 22:24:52
%S A211017 0,0,8,8,24,16,40,104,48,32,168,424,208,96,64,680,1704,848,416,192,
%T A211017 128,2728,6824,3408,1696,832,384,256,10920,27304,13648,6816,3392,1664,
%U A211017 768,512,43688,109924,54608,27296,13632,6784,3328,1536,1024
%N A211017 T(n,k) = total area of all squares and rectangles of area 2^(k-1) after 2^n stages in the toothpick structure of A139250, n>=1, k>=1, assuming the toothpicks have length 2. Triangle read by rows.
%C A211017 All internal regions in the toothpick structure are squares and rectangles. The area of every internal region is a power of 2.
%H A211017 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 A211017 T(n,k) = A211016(n,k)*2^(k-1).
%F A211017 T(n,1) = 4*A020988(n-2), n>=2.
%e A211017 For n = 5 in the toothpick structure after 2^5 stages we have that:
%e A211017 T(5,1) = 168 is the total area of all squares of size 1 X 1.
%e A211017 T(5,2) = 424 is the total area of all rectangles of size 1 X 2.
%e A211017 T(5,3) = 208 is the total area of all squares of size 2 X 2 and of all rectangles of size 1 X 4.
%e A211017 T(5,4) = 96 is the total area of all rectangles of size 2 X 4.
%e A211017 T(5,5) = 64 is the total area of all rectangles of size 2 X 8.
%e A211017 Triangle begins:
%e A211017       0;
%e A211017       0,     8;
%e A211017       8,    24,    16;
%e A211017      40,   104,    48,   32;
%e A211017     168,   424,   208,   96,   64;
%e A211017     680,  1704,   848,  416,  192,  128;
%e A211017    2728,  6824,  3408, 1696,  832,  384, 256;
%e A211017   10920, 27304, 13648, 6816, 3392, 1664, 768, 512;
%Y A211017 Row sums give A211012.
%Y A211017 Cf. A020988, A139250, A160124, A211016, A211018, A211019.
%K A211017 nonn,tabl
%O A211017 1,3
%A A211017 _Omar E. Pol_, Sep 21 2012