This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A160407 #20 Feb 24 2021 02:48:18 %S A160407 1,1,2,2,2,2,4,4,2,2,4,4,4,6,10,8,2,2,4,4,4,6,10,8,4,6,10,10,12,20,26, %T A160407 16,2,2,4,4,4,6,10,8,4,6,10,10,12,20,26,16,4,6,10,10,12,20,26,18,12, %U A160407 20,28,30,42 %N A160407 First differences of toothpick numbers A160406. %C A160407 Number of toothpicks added at n-th stage in the toothpick structure of A160406. %C A160407 From _Omar E. Pol_, Mar 15 2020: (Start) %C A160407 The cellular automaton described in A160406 has word "ab", so the structure of this triangle is as follows: %C A160407 a,b; %C A160407 a,b; %C A160407 a,b,a,b; %C A160407 a,b,a,b,a,b,a,b; %C A160407 a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b; %C A160407 ... %C A160407 The row lengths are the terms of A011782 multiplied by 2, equaling the column 2 of the square array A296612: 2, 2, 4, 8, 16, ... %C A160407 This arrangement has the property that the odd-indexed columns (a) contain numbers of the toothpicks that are parallel to initial toothpick, and the even-indexed columns (b) contain numbers of the toothpicks that are orthogonal to the initial toothpick. %C A160407 For further information about the "word" of a cellular automaton see A296612. (End) %H A160407 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 A160407 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 A160407 From _Omar E. Pol_, Jul 18 2009, Mar 15 2020: (Start) %e A160407 If written as a triangle: %e A160407 1,1; %e A160407 2,2; %e A160407 2,2,4,4; %e A160407 2,2,4,4,4,6,10,8; %e A160407 2,2,4,4,4,6,10,8,4,6,10,10,12,20,26,16; %e A160407 2,2,4,4,4,6,10,8,4,6,10,10,12,20,26,16,4,6,10,10,12,20,26,18,12,20,28,30,42;... %e A160407 (End) %Y A160407 Cf. A011782, A139250, A139251, A153000, A153006, A152980, A160406, A161830, A161831, A296612. %K A160407 nonn %O A160407 1,3 %A A160407 _Omar E. Pol_, May 23 2009 %E A160407 More terms from _N. J. A. Sloane_, Jul 17 2009