Jacek Sandomierz - cp's OEIS frontend

User: Jacek Sandomierz

Jacek Sandomierz has authored 2 sequences.

A308626 Van Eck sequence on a square spiral on a 2-D grid.

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

Jacek Sandomierz, Jun 11 2019

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

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A181391, A308625.

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

A308625 Van Eck sequence in 2-dimensional hexagonal space.

Original entry on oeis.org

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

Offset: 1

Jacek Sandomierz, Jun 11 2019

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

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A181391, A308626.

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

Extended by Charlie Neder, Jun 13 2019

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User: Jacek Sandomierz

A308626 Van Eck sequence on a square spiral on a 2-D grid.

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