A308625 Van Eck sequence in 2-dimensional hexagonal space.

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

Author

Jacek Sandomierz, Jun 11 2019

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A181391, A308626.

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

Extensions

Extended by Charlie Neder, Jun 13 2019