OFFSET
0,3
COMMENTS
Equivalently, a(n) gives the number of toothpicks added at stage n of the construction described in A351837.
For symmetry reasons, all terms except a(1) = 1 are multiples of 4.
LINKS
FORMULA
Empirically:
- a(2^k - 1) = A058922(k-1) for any k >= 2,
- a(2^k) = 2^(k+1) for any k >= 1,
- a(2^k + 1) = 8 for any k >= 2,
- a(2^k + 2) = 12 for any k >= 2.
EXAMPLE
The configuration at stage 4 can be depicted as follows (stars representing ends and toothpicks being labeled with their stage of appearance):
.
* *
| |
4 4
| |
*---3---* *---3---*
| | | |
4 2 2 4
| | | |
* *---1---* *
| | | |
4 2 2 4
| | | |
*---3---* *---3---*
| |
4 4
| |
* *
.
- so a(1) = 1, a(2) = a(3) = 4, a(4) = 8.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Feb 21 2022
STATUS
approved