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

0,6

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<n, k>=1. See example and Link section.

Links

Table of n, a(n) for n=0..64.

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

Example

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        | | | |
...

Crossrefs

Partial sums of A229951.

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

Sequence in context: A062303 A180682 A227426 * A050318 A130841 A002095

Adjacent sequences: A229947 A229948 A229949 * A229951 A229952 A229953

Keyword

nonn

Author

Omar E. Pol, Oct 04 2013

Status

approved