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 A172308 #10 Feb 24 2021 02:48:19 %S A172308 0,1,3,5,7,11,15,17,21,27,33,41,47,59,69,75,79,85,95,107,117,131,145, %T A172308 161,177,195,209,225,237,257,279,287,295,311,329,345,355,371,391,415, %U A172308 441,477,501,533,563,603,631,655 %N A172308 L-toothpick sequence in the first quadrant. %C A172308 The same as A172310 and A172304, but starting from half L-toothpick in the first quadrant. %C A172308 Note that if n is odd then we add the small L-toothpicks to the structure, otherwise we add the large L-toothpicks to the structure. %C A172308 We start at stage 0 with half L-toothpick: A segment from (0,0) to (1,1). %C A172308 At stage 1 we place a small L-toothpick at the exposed toothpick end. %C A172308 At stage 2 we place two large L-toothpicks. %C A172308 At stage 3 we place two small L-toothpicks. %C A172308 At stage 4 we place two large L-toothpicks. %C A172308 And so on... %C A172308 The sequence gives the number of L-toothpicks after n stages. A172309 (the first differences) gives the number of L-toothpicks added at the n-th stage. %H A172308 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 A172308 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> %Y A172308 Cf. A139250, A153000, A160120, A160170, A160172, A161206, A161328, A172304, A172305, A172306, A172307, A172309, A172310, A172311, A172312, A172313. %K A172308 nonn %O A172308 0,3 %A A172308 _Omar E. Pol_, Feb 06 2010 %E A172308 a(17)-a(47) from _Robert Price_, Jun 17 2019