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A275606 Spiral constructed on the nodes of the triangular net such that a(n) = signum(A274920(n)). 7
0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

The structure of the spiral has the following properties:

1) The 1's represent the nodes of the hexagonal net.

2) Every 0 is surrounded by six equidistant 1's.

3) Every 1 is surrounded by three equidistant 0's and three equidistant 1's.

4) Diagonals are periodic sequences with period 3 (A011655).

Also the 1's represent the atoms of carbon in graphene.

LINKS

Table of n, a(n) for n=0..105.

Wikipedia, Graphene

FORMULA

a(n) = A057427(A274920(n)).

EXAMPLE

Illustration of initial terms as a spiral:

.

.                1 - 0 - 1 - 1 - 0 - 1

.               /                     \

.              0   1 - 1 - 0 - 1 - 1   0

.             /   /                 \   \

.            1   1   0 - 1 - 1 - 0   1   1

.           /   /   /             \   \   \

.          1   0   1   1 - 0 - 1   1   0   1

.         /   /   /   /         \   \   \   \

.        0   1   1   0   1 - 1   0   1   1   0

.       /   /   /   /   /     \   \   \   \   \

.      1   1   0   1   1   0 - 1   1   0   1   1

.       \   \   \   \   \         /   /   /   /

.        0   1   1   0   1 - 1 - 0   1   1   0

.         \   \   \   \             /   /   /

.          1   0   1   1 - 0 - 1 - 1   0   1

.           \   \   \                 /   /

.            1   1   0 - 1 - 1 - 0 - 1   1

.             \   \                     /

.              0   1 - 1 - 0 - 1 - 1 - 0

.               \

.                1 - 0 - 1 - 1 - 0 - 1

.

CROSSREFS

Cf. A011655, A057427, A274820, A274821, A274920, A274921, A275610.

Sequence in context: A182067 A196147 A242647 * A211487 A252372 A204447

Adjacent sequences:  A275603 A275604 A275605 * A275607 A275608 A275609

KEYWORD

nonn

AUTHOR

Omar E. Pol, Nov 09 2016

STATUS

approved

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Last modified November 18 01:16 EST 2017. Contains 294837 sequences.