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%I #18 Feb 24 2021 02:48:19
%S 0,0,1,3,4,5,10,17,20,21,25,30,33,40,58,77,84,85,89,94,97,104,121,138,
%T 145,151,164,177,190,222,278,325,340,341,345,350,353,360,377,394,401,
%U 407,420,433,446,478,533,578,593,599,612,625,638,669,720,761,781,806,845,884,942
%N Total number of squares and rectangles at the n-th stage in the corner toothpick structure (see A152890, A153006).
%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(2^k) = (4^k-4)/3 for k >= 2. - _N. J. A. Sloane_, Feb 13 2010.
%Y Partial sums of A168131.
%K nonn
%O 0,4
%A _Omar E. Pol_, Jan 18 2010
%E Edited and extended by _N. J. A. Sloane_, Feb 01 2010
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