|
%I #16 Sep 26 2015 01:17:13
%S 0,0,1,1,3,2,5,13,6,4,21,53,26,12,8,85,213,106,52,24,16,341,853,426,
%T 212,104,48,32,1365,3413,1706,852,424,208,96,64,5461,13653,6826,3412,
%U 1704,848,416,192,128,21845,54613,27306,13652,6824,3408,1696,832,384,256
%N Triangle read by rows: 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, divided by 8, n>=1, k>=1, assuming the toothpicks have length 2.
%C All internal regions in the toothpick structure are squares and rectangles. The area of every internal region is a power of 2.
%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) = A211017(n,k)/8.
%F T(n,1) = A002450(n-2), n>=2.
%e 0;
%e 0, 1;
%e 1, 3, 2;
%e 5, 13, 6, 4;
%e 21, 53, 26, 12, 8;
%e 85, 213, 106, 52, 24, 16;
%e 341, 853, 426, 212, 104, 48, 32;
%e 1365, 3413, 1706, 852, 424, 208, 96, 64;
%e 5461, 13653, 6826, 3412, 1704, 848, 416, 192, 128;
%Y Rows sums give A006516. Right border gives A131577.
%Y Cf. A002450, A072197, A139250, A160124, A211012, A211016, A211017, A211019
%K nonn,tabl
%O 1,5
%A _Omar E. Pol_, Sep 24 2012
|
