A194803 Number of parts that are visible in one of the three views of the shell model of partitions version "Tree" with n shells.

0, 1, 3, 5, 8, 11, 17, 23, 33, 46, 64, 86, 121, 161, 217, 291, 388, 507, 671, 870, 1131, 1458, 1872, 2383, 3042, 3840, 4841, 6076, 7605, 9460, 11765, 14544, 17950, 22073, 27077, 33092, 40395, 49113, 59611, 72162, 87185, 105035, 126366

Offset

0,3

Comments

The physical model shows each part represented by an object, for example using a cube or a cuboid. In this case the small version of the model shows each part as a cube of side 1 which is labeled with the size of the part. On the same way the large version of the model shows each part as a cuboid of sides 1 x 1 x L where L is the size of the part. The cuboid is labeled with the level of the part. For the sum of parts see A194804. For more information about the shell model see A135010 and A194805.

Links

Table of n, a(n) for n=0..42.

Formula

a(n) = n + A138135(n-1) + A138135(n), if n >= 2.

Example

Illustration of one of the three views with seven shells:
1) Small version:
.
Level
1        A182732 <- 6 3 4 2 1 3 5 4 7 -> A182733
2                     3 2 2 1 2 2 3
3                         2 1 2
4                           1
5      Table 2.0            1            Table 2.1
6                           1
7                           1
.
.  A182742  A182982                   A182743  A182983
.  A182992  A182994                   A182993  A182995
.
2) Large version:
.
.                   . . . . 1 . . . .
.                   . . . 1 2 . . . .
.                   . 1 . . 2 1 . . .
.                   . . 1 2 2 . . 1 .
.                   . . . . 2 2 1 . .
.                   1 2 2 3 2 . . . .
.                           2 3 2 2 1
.
The large version shows the parts labeled with the level of the part where "the level of a part" is its position in the partition. In both versions there are 23 parts that are visible, so a(7) = 23. Also using the formula we have a(7) = 7+8+8 = 23.

Crossrefs

Cf. A006128, A096541, A138135, A135010, A138121, A141285, A182732, A182733, A182742, A182743, A182982, A182983, A182992-A182995, A194804, A194805, A210979.

Sequence in context: A371154 A338204 A244031 * A284835 A308266 A320594

Adjacent sequences: A194800 A194801 A194802 * A194804 A194805 A194806

Keyword

nonn

Author

Omar E. Pol, Jan 27 2012

Status

approved