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A228371 First differences of A228370. Also A001511 and A006519 interleaved. 7
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A347967 A090706 A284548 * A176971 A247917 A050935
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Aug 21 2013
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)