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%I #13 Feb 24 2021 02:48:18
%S 0,0,0,1,2,2,4,9,12,12,14,18,20,22,32,47,54,54,56,60,62,64,74,88,94,
%T 96,104,114,120,134,170,209,224,224,226,230,232,234,244,258,264,266,
%U 274,284,290,304,340,378,392,394,402,412,418,432,466,500,514
%N Total number of squares and rectangles in the toothpick structure after n stages, divided by 2. (See A139250).
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.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(n) = A160124(n)/2. - _Nathaniel Johnston_, Apr 12 2011
%Y Cf. A139250, A159786, A159787, A159788, A159789, A160124, A160125, A160127.
%K nonn
%O 0,5
%A _Omar E. Pol_, May 03 2009
%E Terms beyond a(10) from _Nathaniel Johnston_, Apr 12 2011
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