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A173531 a(0)=0: For n>0, a(n) = A060632(n)*A060632(n-1).

%I A173531 #11 Jan 11 2024 10:58:22
%S A173531 0,1,2,4,4,4,8,16,8,4,8,16,16,16,32,64,16,4,8,16,16,16,32,64,32,16,32,
%T A173531 64,64,64,128,256,32,4,8,16,16,16,32,64,32,16,32,64,64,64,128,256,64,
%U A173531 16,32,64,64,64,128,256,128,64,128,256,256
%N A173531 a(0)=0: For n>0, a(n) = A060632(n)*A060632(n-1).
%C A173531 First differences of A173530.
%C A173531 Number of triangles (Or V-toothpicks, or L-toothpicks, etc.) added in the three-dimensional structure of A173530 at the n-th stage.
%H A173531 Michael De Vlieger, <a href="/A173531/b173531.txt">Table of n, a(n) for n = 0..16383</a>
%H A173531 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 A173531 Christina Talar Bekaroğlu, <a href="https://scholarworks.calstate.edu/concern/theses/bk128j63v">Analyzing Dynamics of Larger than Life: Impacts of Rule Parameters on the Evolution of a Bug's Geometry</a>, Master's thesis, Calif. State Univ. Northridge (2023). See p. 92.
%H A173531 Michael De Vlieger, <a href="/A173531/a173531.png">Scatterplot of Log_2 a(n)</a> for n = 1..1024.
%H A173531 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>
%e A173531 If written as a triangle, begins:
%e A173531 0;
%e A173531 1;
%e A173531 2;
%e A173531 4,4;
%e A173531 4,8,16,8;
%e A173531 4,8,16,16,16,32,64,16;
%e A173531 4,8,16,16,16,32,64,32,16,32,64,64,64,128,256,32;
%e A173531 4,8,16,16,16,32,64,32,16,32,64,64,64,128,256,64,16,32,64,64,64,128,256,128,...
%t A173531 Prepend[Times @@@ Partition[Array[2^DigitCount[Floor[#/2], 2, 1] &, 120, 0], 2, 1], 0] (* _Michael De Vlieger_, Jan 11 2024 *)
%Y A173531 Cf. A001316, A047999, A060632, A139250, A139251, A161207, A172311, A173530, A173532.
%K A173531 nonn
%O A173531 0,3
%A A173531 _Omar E. Pol_, Oct 10 2010