A210990 Total area of the shadows of the three views of the shell model of partitions with n regions.

0, 3, 10, 21, 26, 44, 51, 75, 80, 92, 99, 136, 143, 157, 166, 213, 218, 230, 237, 260, 271, 280, 348, 355, 369, 378, 403, 410, 427, 438, 526, 531, 543, 550, 573, 584, 593, 631, 640, 659, 672, 683, 804, 811, 825, 834, 859, 866, 883, 894, 938, 949, 958

Offset

0,2

Comments

Each part is represented by a cuboid of sides 1 X 1 X k where k is the size of the part. For the definition of "regions of n" see A206437.

Links

Table of n, a(n) for n=0..52.

Formula

a(n) = A182244(n) + A182727(n) + A182181(n), n >= 1.

a(A000041(n)) = 2*A006128(n) + A066186(n).

Example

For n = 11 the three views of the shell model of partitions with 11 regions look like this:
.
.   A182181(11) = 35            A182244(11) = 66
.
.   6                             * * * * * 6
.   3 3                      P    * * 3 * * 3
.   2   4                    a    * * * 4 * 2
.   2   2 2                  r    * 2 * 2 * 2
.   1       5                t    * * * * 5 1
.   1       2 3              i    * * 3 * 2 1
.   1       1   4            t    * * * 4 1 1
.   1       1   2 2          i    * 2 * 2 1 1
.   1       1   1   3        o    * * 3 1 1 1
.   1       1   1   1 2      n    * 2 1 1 1 1
.   1       1   1   1 1 1    s    1 1 1 1 1 1
. <------- Regions ------         ------------> N
.                            L
.                            a    1
.                            r    * 2
.                            g    * * 3
.                            e    * 2
.                            s    * * * 4
.                            t    * * 3
.                                 * * * * 5
.                            p    * 2
.                            a    * * * 4
.                            r    * * 3
.                            t    * * * * * 6
.                            s
.                               A182727(11) = 35
.
The areas of the shadows of the three views are A182244(11) = 66, A182181(11) = 35 and A182727(11) = 35, therefore the total area of the three shadows is 66+35+35 = 136, so a(11) = 136.

Crossrefs

Other versions: A207380, A210970, A210979, A210980, A210991.

Cf. A135010, A138121, A141285, A194446, A182181, A182727, A186114, A206437.

Sequence in context: A196166 A073604 A370032 * A004194 A097590 A289183

Adjacent sequences: A210987 A210988 A210989 * A210991 A210992 A210993

Keyword

nonn

Author

Omar E. Pol, Apr 23 2012

Status

approved