A229950 Total number of toothpicks after n-th stage in a toothpick structure in which the toothpicks represent the 1's of triangle A229940.

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, 36, 37, 40, 41, 44, 45, 49, 52, 56, 57, 61, 64, 68, 69, 73, 75, 79, 81, 85, 88, 92, 92, 96, 99, 104, 107, 112, 115, 120, 122, 127, 131, 136, 137, 142, 146, 151, 153

Offset: 0

Author

Omar E. Pol, Oct 04 2013

Keywords

• nonn

Comments

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       1                         2
5       2         |
6       2                         2
7       3         |
8       3                         3
9       5         | |
10      6           |             2
11      8         | |
12      8                         4
13      10        | |
14      11          |             2
15      13        | |
16      13                        4
17      15        | |
18      16          |             3
19      19        | | |
20      20            |           4
21      23        | | |
22      25          | |           2
23      28        | | |
24      28                        6
25      31        | | |
26      33          | |           2
27      36        | | |
28      37            |           4
29      40        | | |
30      41          |             4
31      44        | | |
32      45            |           5
33      49        | | | |
...
		

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

Partial sums of A229951.

Cf. A000005, A139250, A229940, A229942, A229951.