A228371 First differences of A228370. Also A001511 and A006519 interleaved.

1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 5, 16, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 6, 32, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 5, 16, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 7, 64

Offset

1,3

Comments

Number of toothpicks added at n-th stage to the toothpick structure (related to integer compositions) of A228370.

The equivalent sequence for integer partitions is A220517.

Links

Table of n, a(n) for n=1..128.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to toothpick sequences

Formula

a(2n-1) = A001511(n), n >= 1. a(2n) = A006519(n), n >= 1.

Example

Illustration of the structure after 32 stages. The diagram represents the 16 compositions of 5. The k-th horizontal line segment has length A001511(k) equals the largest part of the k-th region. The k-th vertical line segment has length A006519(k) equals the number of parts of the k-th region.
.      _ _ _ _ _
16     _        |
15     _|_      |
14     _  |     |
13     _|_|_    |
12     _    |   |
11     _|_  |   |
10     _  | |   |
9      _|_|_|_  |
8      _      | |
7      _|_    | |
6      _  |   | |
5      _|_|_  | |
4      _    | | |
3      _|_  | | |
2      _  | | | |
1       | | | | |
.
Written as an irregular triangle the sequence begins:
  1,1;
  2,2;
  1,1,3,4;
  1,1,2,2,1,1,4,8;
  1,1,2,2,1,1,3,4,1,1,2,2,1,1,5,16;
  1,1,2,2,1,1,3,4,1,1,2,2,1,1,4,8,1,1,2,2,1,1,3,4,1,1,2,2,1,1,6,32;
  ...

Prog

(Python)
def A228371(n): return ((m:=(n>>1)+1)&-m).bit_length() if n&1 else (m:=n>>1)&-m # Chai Wah Wu, Jul 14 2022

Crossrefs

Row lengths give 2*A011782. Right border gives A000079.

Cf. A001511, A006519, A139250, A139251, A206437, A220517, A228370.

Sequence in context: A347967 A090706 A284548 * A176971 A247917 A050935

Adjacent sequences: A228368 A228369 A228370 * A228372 A228373 A228374

Keyword

nonn,tabf

Author

Omar E. Pol, Aug 21 2013

Status

approved