%N Total area of all squares and rectangles after n-th stage in the toothpick structure of A139250, assuming the toothpicks have length 2.
%C Note that if n > 1 is a power of 2 then a(n) = n^2 - 2n.
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="http://neilsloane.com/doc/tooth.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 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 a(2^k) = A211012(k). - _Omar E. Pol_, Sep 25 2012
%Y Cf. A139250, A139251, A159787, A159788, A159789, A159796.
%A _Omar E. Pol_, Apr 28 2009
%E More terms from _Omar E. Pol_, Sep 25 2012