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%I #15 Nov 16 2013 14:20:36
%S 0,0,0,1,1,2,2,3,3,5,6,8,8,10,11,13,13,15,16,19,20,23,25,28,28,31,33,
%T 36,37,40,41,44,45,49,52,56,57,61,64,68,69,73,75,79,81,85,88,92,92,96,
%U 99,104,107,112,115,120,122,127,131,136,137,142,146,151,153
%N Total number of toothpicks after n-th stage in a toothpick structure in which the toothpicks represent the 1's 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 1 2
%e 5 2 |
%e 6 2 2
%e 7 3 |
%e 8 3 3
%e 9 5 | |
%e 10 6 | 2
%e 11 8 | |
%e 12 8 4
%e 13 10 | |
%e 14 11 | 2
%e 15 13 | |
%e 16 13 4
%e 17 15 | |
%e 18 16 | 3
%e 19 19 | | |
%e 20 20 | 4
%e 21 23 | | |
%e 22 25 | | 2
%e 23 28 | | |
%e 24 28 6
%e 25 31 | | |
%e 26 33 | | 2
%e 27 36 | | |
%e 28 37 | 4
%e 29 40 | | |
%e 30 41 | 4
%e 31 44 | | |
%e 32 45 | 5
%e 33 49 | | | |
%e ...
%Y Partial sums of A229951.
%Y Cf. A000005, A139250, A229940, A229942, A229951.
%K nonn
%O 0,6
%A _Omar E. Pol_, Oct 04 2013
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