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

%I A228371 #18 Jul 16 2022 01:04:54
%S A228371 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 A228371 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 A228371 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 A228371 First differences of A228370. Also A001511 and A006519 interleaved.
%C A228371 Number of toothpicks added at n-th stage to the toothpick structure (related to integer compositions) of A228370.
%C A228371 The equivalent sequence for integer partitions is A220517.
%H A228371 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 A228371 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F A228371 a(2n-1) = A001511(n), n >= 1. a(2n) = A006519(n), n >= 1.
%e A228371 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 A228371 .      _ _ _ _ _
%e A228371 16     _        |
%e A228371 15     _|_      |
%e A228371 14     _  |     |
%e A228371 13     _|_|_    |
%e A228371 12     _    |   |
%e A228371 11     _|_  |   |
%e A228371 10     _  | |   |
%e A228371 9      _|_|_|_  |
%e A228371 8      _      | |
%e A228371 7      _|_    | |
%e A228371 6      _  |   | |
%e A228371 5      _|_|_  | |
%e A228371 4      _    | | |
%e A228371 3      _|_  | | |
%e A228371 2      _  | | | |
%e A228371 1       | | | | |
%e A228371 .
%e A228371 Written as an irregular triangle the sequence begins:
%e A228371   1,1;
%e A228371   2,2;
%e A228371   1,1,3,4;
%e A228371   1,1,2,2,1,1,4,8;
%e A228371   1,1,2,2,1,1,3,4,1,1,2,2,1,1,5,16;
%e A228371   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 A228371   ...
%o A228371 (Python)
%o A228371 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 A228371 Row lengths give 2*A011782. Right border gives A000079.
%Y A228371 Cf. A001511, A006519, A139250, A139251, A206437, A220517, A228370.
%K A228371 nonn,tabf
%O A228371 1,3
%A A228371 _Omar E. Pol_, Aug 21 2013