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 A296610 #28 Apr 11 2019 22:47:12 %S A296610 0,1,2,3,4,5,7,10,13,15,18,21,25,31,36,38,41,44,48,54,61,67,75,80,88, %T A296610 100,110,113,116,119,123,129,136,142,150,157,167,183,199,210,220,225, %U A296610 233,245,261,276,295,306,325,351,372,378,381,384,388,394,401,407,415,422,432,448,464,475,485,492,502,518,538,559,585 %N A296610 Toothpick sequence on triangular grid in an infinite 60-degree wedge (see Comments lines for precise definition). %C A296610 The rules are the same as the rules of A296510 (the toothpick sequence on triangular grid) but here we are in a 60-degree wedge. For the position of the initial toothpicks see the example. %C A296610 a(n) gives the total number of toothpicks in the structure after n-th stage. %C A296610 A296611, the first differences, gives the number of toothpicks added at n-th stage. %C A296610 The "word" of this cellular automaton is "abc", the same as the word of A296510. For more information about the word of cellular automata see A296612. %H A296610 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> %H A296610 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a> %H A296610 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a> %e A296610 Illustration of the 60-degree wedge of the triangular grid and the first three terms of the sequence: %e A296610 . %e A296610 /\ /\ /\ %e A296610 / \ / /\ / /\ %e A296610 / \ / / \ /_/_ \ %e A296610 / \ / \ / \ %e A296610 / \ / \ / \ %e A296610 / \ / \ / \ %e A296610 n: 0 1 2 %e A296610 a(n): 0 1 2 %e A296610 . %e A296610 At stage 0 there are no toothpicks in the wedge, so a(0) = 0. %e A296610 At stage 1 we add a toothpick of length 2, so a(1) = 1. %e A296610 At stage 2 we add a toothpick in horizontal position, so a(2) = a(1) + 1 = 1 + 1 = 2. Note that in the structure there is a trapeze of area 5. %e A296610 Then, at stage 3 we add a toothpick such that a equilateral triangle of area 1 appears in the wedge. %e A296610 Then, at stage 4 we add a toothpick placed in the same position as the first toothpick. %e A296610 And so on. %Y A296610 Cf. A139250, A296510, A296611, A296612. %K A296610 nonn %O A296610 0,3 %A A296610 _Omar E. Pol_, Mar 02 2019