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A308626
Van Eck sequence on a square spiral on a 2-D grid.
2
0, 0, 1, 0, 1, 2, 0, 2, 2, 1, 3, 0, 2, 4, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,6
COMMENTS
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
FORMULA
G.f.: x^3*(1 - x + x^2 + x^3 - 2*x^4 + 2*x^5 - x^7 + 2*x^8 - 3*x^9 + 2*x^10 + 2*x^11 - 4*x^12 + x^13)/(1 - x). - Elmo R. Oliveira, Aug 03 2024
CROSSREFS
Sequence in context: A029314 A071635 A156643 * A268755 A128664 A003823
KEYWORD
nonn,easy
AUTHOR
Jacek Sandomierz, Jun 11 2019
STATUS
approved