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 A168112 #12 Feb 24 2021 02:48:18 %S A168112 0,1,2,4,7,10,13,19,26,32,35,41,48,56,65,81,98,108,111,117,124,132, %T A168112 141,157,174,186,195,211,230,252,283,329,370,388,391,397,404,412,421, %U A168112 437,454,466,475,491,510,532,563,609,650,670 %N A168112 Toothpick sequence starting with a straight line, with angle = Pi/4, from which protrudes a half toothpick. %C A168112 On the infinite square grid, we start at round 0 drawing a straight line, with angle = Pi/4, from which protrudes a half toothpick. %C A168112 At round 1 we place an orthogonal toothpick centered at the end. %C A168112 In each subsequent round, for every exposed toothpick end, place an orthogonal toothpick centered at that end. %C A168112 The sequence gives the number of toothpicks after n rounds. %C A168112 See also A168113, the first differences. %C A168112 For more information see A139250, which is the main entry for this sequence. %H A168112 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 A168112 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 A168112 a(n) = A160730(n)/2. [From _Nathaniel Johnston_, Mar 28 2011] %Y A168112 Cf. A139250, A139251, A153000, A153006, A160406, A168113, A168114. %K A168112 nonn %O A168112 0,3 %A A168112 _Omar E. Pol_, Dec 07 2009 %E A168112 Terms after a(34) from _Nathaniel Johnston_, Mar 28 2011