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 A152978 #12 Feb 24 2021 02:48:18 %S A152978 1,1,1,2,3,2,1,2,3,3,4,7,8,4,1,2,3,3,4,7,8,5,4,7,9,10,15,22,20,8,1,2, %T A152978 3,3,4,7,8,5,4,7,9,10,15,22,20,9,4,7,9,10,15,22,21,14,15,23,28,35,52, %U A152978 64,48,16,1,2,3,3,4,7,8,5,4,7,9,10,15,22,20,9,4,7,9,10,15,22,21,14,15,23 %N A152978 a(n) = A139251(n+2)/4 = A152968(n+1)/2. %C A152978 Also, first differences of toothpick numbers A153000. %H A152978 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a> %H A152978 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 A152978 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 A152978 G.f.: (1+x)*(Prod(1+x^(2^k-1)+2*x^(2^k),k=1..oo)-1)/(1+2*x). - _N. J. A. Sloane_, May 20 2009 %e A152978 If written as a triangle, begins: %e A152978 .1,1; %e A152978 .1,2,3,2; %e A152978 .1,2,3,3,4,7,8,4; %e A152978 .1,2,3,3,4,7,8,5,4,7,9,10,15,22,20,8; %e A152978 .... %e A152978 Rows converge to A152980. %e A152978 It appears that row sums give A004171. [From _Omar E. Pol_, May 25 2010] %Y A152978 Cf. toothpick sequence A139250. %Y A152978 Cf. A139251, A139252, A139560, A152968, A152973. %Y A152978 Cf. A152980, A152998, A153000, A153001, A153003, A153004, A153006. %Y A152978 Cf. A004171. [From _Omar E. Pol_, May 25 2010] %K A152978 nonn,easy %O A152978 1,4 %A A152978 _Omar E. Pol_, Dec 16 2008, Dec 20 2008 %E A152978 More terms from _Omar E. Pol_, Jul 26 2009