A351838 First differences of A351837.

0, 1, 4, 4, 8, 8, 12, 16, 16, 8, 12, 20, 24, 28, 40, 48, 32, 8, 12, 20, 24, 28, 40, 52, 40, 28, 44, 64, 76, 96, 128, 128, 64, 8, 12, 20, 24, 28, 40, 52, 40, 28, 44, 64, 76, 96, 128, 132, 72, 28, 44, 64, 76, 96, 132, 144, 108, 100, 152, 204, 248, 320, 384, 320

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

Rémy Sigrist, Table of n, a(n) for n = 0..8194

Rémy Sigrist, Illustration of the structure at stage 16

Rémy Sigrist, PARI program

Index entries for sequences related to cellular automata

Index entries for sequences related to toothpick sequences

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

Cf. A058922, A139251, A351837.

Sequence in context: A146890 A168273 A278933 * A328527 A145447 A204989

Adjacent sequences: A351835 A351836 A351837 * A351839 A351840 A351841

Keyword

nonn

Author

Rémy Sigrist, Feb 21 2022

Status

approved