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

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, 100, 110, 113, 116, 119, 123, 129, 136, 142, 150, 157, 167, 183, 199, 210, 220, 225, 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

Offset: 0

Author

Omar E. Pol, Mar 02 2019

Keywords

• nonn

Comments

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.

a(n) gives the total number of toothpicks in the structure after n-th stage.

A296611, the first differences, gives the number of toothpicks added at n-th stage.

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.

Examples

			Illustration of the 60-degree wedge of the triangular grid and the first three terms of the sequence:
.
           /\             /\             /\
          /  \           / /\           / /\
         /    \         / /  \         /_/_ \
        /      \       /      \       /      \
       /        \     /        \     /        \
      /          \   /          \   /          \
n:          0              1              2
a(n):       0              1              2
.
At stage 0 there are no toothpicks in the wedge, so a(0) = 0.
At stage 1 we add a toothpick of length 2, so a(1) = 1.
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.
Then, at stage 3 we add a toothpick such that a equilateral triangle of area 1 appears in the wedge.
Then, at stage 4 we add a toothpick placed in the same position as the first toothpick.
And so on.
		

Links

• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to cellular automata
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A139250, A296510, A296611, A296612.