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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.

A296610 Toothpick sequence on triangular grid in an infinite 60-degree wedge (see Comments lines for precise definition).

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%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