OFFSET
0,3
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.
LINKS
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 02 2019
STATUS
approved