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%I #18 Jul 16 2022 01:04:54
%S 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,
%T 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,
%U 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
%N First differences of A228370. Also A001511 and A006519 interleaved.
%C Number of toothpicks added at n-th stage to the toothpick structure (related to integer compositions) of A228370.
%C The equivalent sequence for integer partitions is A220517.
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F a(2n-1) = A001511(n), n >= 1. a(2n) = A006519(n), n >= 1.
%e 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.
%e . _ _ _ _ _
%e 16 _ |
%e 15 _|_ |
%e 14 _ | |
%e 13 _|_|_ |
%e 12 _ | |
%e 11 _|_ | |
%e 10 _ | | |
%e 9 _|_|_|_ |
%e 8 _ | |
%e 7 _|_ | |
%e 6 _ | | |
%e 5 _|_|_ | |
%e 4 _ | | |
%e 3 _|_ | | |
%e 2 _ | | | |
%e 1 | | | | |
%e .
%e Written as an irregular triangle the sequence begins:
%e 1,1;
%e 2,2;
%e 1,1,3,4;
%e 1,1,2,2,1,1,4,8;
%e 1,1,2,2,1,1,3,4,1,1,2,2,1,1,5,16;
%e 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;
%e ...
%o (Python)
%o 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
%Y Row lengths give 2*A011782. Right border gives A000079.
%Y Cf. A001511, A006519, A139250, A139251, A206437, A220517, A228370.
%K nonn,tabf
%O 1,3
%A _Omar E. Pol_, Aug 21 2013
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