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A229951 Number of toothpicks added at n-th stage to the toothpick structure of A229950.

%I A229951 #16 Nov 16 2013 13:38:26
%S A229951 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 A229951 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 A229951 3,5,3,5,1,6,5,6,4,6,4,6,2,6,5,6,2,6,5
%N A229951 Number of toothpicks added at n-th stage to the toothpick structure of A229950.
%C A229951 Essentially the first differences of A229950.
%C A229951 Also [0, 0, 0] together the row sums of triangle A229940.
%C A229951 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 A229951 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 A229951 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 A229951 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%e A229951 Illustration of initial terms:
%e A229951 ----------------------------------------
%e A229951 n      a(n)       Diagram       A000005
%e A229951 ----------------------------------------
%e A229951 0       0
%e A229951 1       0
%e A229951 2       0                          1
%e A229951 3       1         |
%e A229951 4       0                          2
%e A229951 5       1         |
%e A229951 6       0                          2
%e A229951 7       1         |
%e A229951 8       0                          3
%e A229951 9       2         | |
%e A229951 10      1           |              2
%e A229951 11      2         | |
%e A229951 12      0                          4
%e A229951 13      2         | |
%e A229951 14      1           |              2
%e A229951 15      2         | |
%e A229951 16      0                          4
%e A229951 17      2         | |
%e A229951 18      1           |              3
%e A229951 19      3         | | |
%e A229951 20      1             |            4
%e A229951 21      3         | | |
%e A229951 22      2           | |            2
%e A229951 23      3         | | |
%e A229951 24      0                          6
%e A229951 25      3         | | |
%e A229951 26      2           | |            2
%e A229951 27      3         | | |
%e A229951 28      1             |            4
%e A229951 29      3         | | |
%e A229951 30      1           |              4
%e A229951 31      3         | | |
%e A229951 32      1             |            5
%e A229951 33      4         | | | |
%e A229951 ...
%Y A229951 Cf. A000005, A139250, A139251, A229940, A229942, A229950.
%K A229951 nonn,tabf
%O A229951 0,10
%A A229951 _Omar E. Pol_, Oct 04 2013