|
| |
|
|
A308625
|
|
Van Eck sequence in 2-dimensional hexagonal space.
|
|
2
|
|
|
|
0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 2, 3, 3, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,6
|
|
|
COMMENTS
|
Fill a board made from hexagonal cells with numbers using the following rules:
- write a 0 in the starting cell;
- if the number just written had not previously been on the board then the next number is 0;
- otherwise, the next number is the distance from its closest occurrence, counting cells you need to pass through to reach it.
______ ______
/ \ / \
/ \ / \
______/ \______/ \______
/ \ / \ / \
/ \ / \ / \
/ \______/ 2 \______/ \
\ / \ . . / \ /
\ / .\ / . \ /
\______/ 1 \______/ 3 \______/
/ \ . / \ . / \
/ \ . / \ / . \
/ 1 \___.__/ 0 \______/ 0 \
\ . / . \ . . / \ . /
\ . / . \ . / . \ . /
\___.__/ 0 \___.__/ 1 \___.__/
/ . \ . / ^ \ . / . \
/ . \ . / | \ . / . \
/ 1 \___.__/ 0 \___.__/ 2 \
\ . / . \ START / . \ . /
\ . / . \ / . \ . /
\___.__/ 2 \______/ 0 \___.__/
/ . \ . / \ . / . \
/ . \ / . .\ / . \
/ 1 \______/ 1 \______/ 3 \
\ . / \ / \ . /
\ / . \ / .\ /
\______/ 1 \______/ 3 \______/
/ \ . / \ . / \
/ \ / . .\ / \
/ \______/ 1 \______/ \
\ / \ / \ /
\ / \ / \ /
\______/ \______/ \______/
.
a(n) = 1 for all n > 15, because the previous 1 will always be adjacent to another 1. - Charlie Neder, Jun 11 2019
|
|
|
LINKS
|
|
|
|
FORMULA
|
G.f.: x^3*(1 - x + x^2 + x^3 - 2*x^4 + x^5 + x^6 + x^7 - 3*x^8 + 2*x^9 + x^10 - 2*x^12)/(1 - x). - Elmo R. Oliveira, Aug 03 2024
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
