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 A152968 #11 Feb 24 2021 02:48:18 %S A152968 1,2,2,2,4,6,4,2,4,6,6,8,14,16,8,2,4,6,6,8,14,16,10,8,14,18,20,30,44, %T A152968 40,16,2,4,6,6,8,14,16,10,8,14,18,20,30,44,40,18,8,14,18,20,30,44,42, %U A152968 28,30,46,56,70,104,128,96,32,2 %N A152968 a(n) = A139251(n+1)/2. %C A152968 Also, first differences of toothpicks numbers A152998. [From _Omar E. Pol_, Jan 02 2009] %H A152968 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 A152968 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 A152968 Write n = 2^i +j, 0 <= j < 2^i; then a(n) = Sum_k 2^(wt(j+k)-k)*binomial(wt(j+k),k). except that a(2^r-1) = 2^(r-1). - _N. J. A. Sloane_, Jun 03 2009, Jul 16 2009 %F A152968 G.f.: x*(Prod(1+x^(2^k-1)+2*x^(2^k),k=0..oo)-1)/(1+2*x). - _N. J. A. Sloane_, Jun 05 2009 %e A152968 Triangle begins: %e A152968 .1; %e A152968 .2,2; %e A152968 .2,4,6,4; %e A152968 .2,4,6,6,8,14,16,8; %e A152968 .2,4,6,6,8,14,16,10,8,14,18,20,30,44,40,16; %e A152968 .... %e A152968 Rows approach A151688. - _N. J. A. Sloane_, Jun 03 2009 %Y A152968 Cf. A139250, A139251, A139252, A152978, A152980, A153006, A152998. %K A152968 nonn %O A152968 1,2 %A A152968 _Omar E. Pol_, Dec 16 2008, Dec 20 2008