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

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, 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, 3, 5, 3, 5, 1, 6, 5, 6, 4, 6, 4, 6, 2, 6, 5, 6, 2, 6, 5

Offset: 0

Author

Omar E. Pol, Oct 04 2013

Keywords

• nonn
• tabf

Comments

Essentially the first differences of A229950.

Also [0, 0, 0] together the row sums of triangle A229940.

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=1. See example and Link section.

Examples

			Illustration of initial terms:
----------------------------------------
n      a(n)       Diagram       A000005
----------------------------------------
0       0
1       0
2       0                          1
3       1         |
4       0                          2
5       1         |
6       0                          2
7       1         |
8       0                          3
9       2         | |
10      1           |              2
11      2         | |
12      0                          4
13      2         | |
14      1           |              2
15      2         | |
16      0                          4
17      2         | |
18      1           |              3
19      3         | | |
20      1             |            4
21      3         | | |
22      2           | |            2
23      3         | | |
24      0                          6
25      3         | | |
26      2           | |            2
27      3         | | |
28      1             |            4
29      3         | | |
30      1           |              4
31      3         | | |
32      1             |            5
33      4         | | | |
...
		

Links

• Omar E. Pol, Illustration of initial terms of the divisor function (A000005), see the third picture.
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A000005, A139250, A139251, A229940, A229942, A229950.