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Fill a 2-dimensional board made from square cells with numbers using the following rules:

- start from 0;

- if the number just written is new then the next number is 0;

- if the number just written was present on the board before, the next number is the distance from its closest occurrence, counting cells you need to pass through to reach it

.

1 0---->2---->2---->1

^ ^ |

| | |

| | v

1 2 0---->0 3

^ ^ Start | |

| | | |

| | v v

1 1<----0<----1 0

^ |

| |

| v

1<----1<----0<----4<----2

.

a(n) = 1 for all n >= 17 because the previous 1 will always be adjacent to another 1. The version of this sequence using the Moore neighborhood (vertex adjacency) consists of 0, 0, 1, 0, 1, 2, 0, 1, 2, 2, and then an infinite number of 1's. - Charlie Neder, Jun 11 2019

For a given lattice, the Van Eck sequence over that lattice is the unique sequence of nonnegative integers such that, if all equal terms are connected by "bridges" that travel between adjacent faces, then each term is the length of the bridge connecting the previous term to a term with lower index, or 0 if no such bridge exists. Generally, the Van Eck sequence of a given lattice is not unique since it depends on the path that the sequence takes through the lattice. This sequence uses a spiral, as in A308625 and A308626, and appears as follows, starting at the cell in parentheses facing upward and traveling clockwise:

--------------------------------

\ / \ / \ 3 / \ 1 / \ / \

.\ / \ / 3 \ / 1 \ / 1 \ / \

--------------------------------

./ \ / \ 2 / \ 1 / \ 1 / \ /

/ \ / 0 \ / 0 \ / 0 \ / 1 \ /

--------------------------------

\ / \ 3 / \(0)/ \ 2 / \ 1 / \

.\ / \ / 2 \ / 0 \ / 1 \ / \

--------------------------------

./ \ / \ 0 / \ 1 / \ 1 / \ /

/ \ / \ / 4 \ / 1 \ / \ /

--------------------------------

Note: This sequence uses the definition that two cells are adjacent if they share an edge. Allowing vertex adjacency makes a very boring sequence: 0, 0, 1, and 0, followed by an infinite string of 1's.

a(n) = 1 for all n >= 17, since the previous 1 will always be adjacent to another 1. The Van Eck-type sequences for the square and hexagonal lattices end similarly.