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A210990
Total area of the shadows of the three views of the shell model of partitions with n regions.
8
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.
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.
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 23 2012
STATUS
approved