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A210979 Total area of the shadows of the three views of the version "Tree" of the shell model of partitions with n shells. 7
0, 3, 8, 15, 27, 42, 69, 102, 155, 225, 327, 458, 652, 894, 1232, 1669, 2257, 2999, 3996, 5242, 6877, 8928, 11564, 14845, 19045, 24223, 30756, 38815, 48877, 61195, 76496, 95124, 118067, 145930, 179991, 221160, 271268, 331538, 404463, 491948, 597253 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The physical model shows each part of a partition as an object, for example; a cube of side 1 which is labeled with the size of the part. Note that on the branches of the tree each column contains parts of the same size, as a periodic structure. For the large version of this model see A210980.

LINKS

Table of n, a(n) for n=0..40.

FORMULA

a(n) = A006128(n) + A194803(n) + A194805(n).

EXAMPLE

For n = 7 the three views of the shell model of partitions version "tree" with seven shells looks like this:

.

.         A194805(7) = 25        A006128(7) = 54

.

.                        7       7

.                      4         4 3

.                    5           5 2

.                  3             3 2 2

.        6       1               6 1

.          3     1               3 3 1

.            4   1               4 2 1

.              2 1               2 2 2 1

.                1   5           5 1 1

.                1 3             3 2 1 1

.            4   1               4 1 1 1

.              2 1               2 2 1 1 1

.                1 3             3 1 1 1 1

.              2 1               2 1 1 1 1 1

.                1               1 1 1 1 1 1 1

-------------------------------------------------

.

.        6 3 4 2 1 3 5 4 7

.          3 2 2 1 2 2 3

.              2 1 2

.                1

.                1

.                1

.                1

.

.         A194803(7) = 23

.

The areas of the shadows of the three views are A006128(7) = 54, A194803(7) = 23 and A194805(7) = 25, therefore the total area of the three shadows is 54+23+25 = 102, so a(7) = 102.

CROSSREFS

Other versions: A207380, A210970, A210980, A210990, A210991.

Cf. A006128, A135010, A138121, A182703, A194803, A194805.

Sequence in context: A109900 A034828 A081276 * A047837 A047873 A036419

Adjacent sequences:  A210976 A210977 A210978 * A210980 A210981 A210982

KEYWORD

nonn

AUTHOR

Omar E. Pol, Apr 28 2012

STATUS

approved

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Last modified May 19 21:29 EDT 2019. Contains 323410 sequences. (Running on oeis4.)