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%I #16 Nov 16 2013 13:38:26
%S 0,0,0,1,0,1,0,1,0,2,1,2,0,2,1,2,0,2,1,3,1,3,2,3,0,3,2,3,1,3,1,3,1,4,
%T 3,4,1,4,3,4,1,4,2,4,2,4,3,4,0,4,3,5,3,5,3,5,2,5,4,5,1,5,4,5,2,5,3,5,
%U 3,5,3,5,1,6,5,6,4,6,4,6,2,6,5,6,2,6,5
%N Number of toothpicks added at n-th stage to the toothpick structure of A229950.
%C Essentially the first differences of A229950.
%C Also [0, 0, 0] together the row sums of triangle A229940.
%C The toothpick structure has the property that the number of exposed endpoints in the row 2k equals the number of divisors of k, if 1<2k<n, k>=1. See example and Link section.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv13.jpg">Illustration of initial terms of the divisor function (A000005)</a>, see the third picture.
%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>
%e Illustration of initial terms:
%e ----------------------------------------
%e n a(n) Diagram A000005
%e ----------------------------------------
%e 0 0
%e 1 0
%e 2 0 1
%e 3 1 |
%e 4 0 2
%e 5 1 |
%e 6 0 2
%e 7 1 |
%e 8 0 3
%e 9 2 | |
%e 10 1 | 2
%e 11 2 | |
%e 12 0 4
%e 13 2 | |
%e 14 1 | 2
%e 15 2 | |
%e 16 0 4
%e 17 2 | |
%e 18 1 | 3
%e 19 3 | | |
%e 20 1 | 4
%e 21 3 | | |
%e 22 2 | | 2
%e 23 3 | | |
%e 24 0 6
%e 25 3 | | |
%e 26 2 | | 2
%e 27 3 | | |
%e 28 1 | 4
%e 29 3 | | |
%e 30 1 | 4
%e 31 3 | | |
%e 32 1 | 5
%e 33 4 | | | |
%e ...
%Y Cf. A000005, A139250, A139251, A229940, A229942, A229950.
%K nonn,tabf
%O 0,10
%A _Omar E. Pol_, Oct 04 2013
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