OFFSET
0,2
COMMENTS
EXAMPLE
For n = 11 the three views of the shell model of partitions with 11 regions look like this:
.
.
. 1 1
. 1 1
. 1 1
. 1 1
. 1 1 1 1
. 1 1 1 1
. 1 1 1 1 1 1
. 2 1 1 1 1 2
. 2 1 1 1 1 1 1 2
. 3 2 2 2 1 1 1 1 2 2 3
. 6 3 4 2 5 3 4 2 3 2 1 1 2 3 4 5 6
. <------- 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 A182181(11) = 35, A182727(11) = 35 and A210692(11) = 29, therefore the total area of the three shadows is 35+35+29 = 99, so a(11) = 99.
Since n = 11 is a partition number A000041 we can see that the rotated structure with 11 regions shows each row as a partition of 6 because A000041(6) = 11. See below:
.
. 6
. 3 3
. 4 2
. 2 2 2
. 5 1
. 3 2 1
. 4 1 1
. 2 2 1 1
. 3 1 1 1
. 2 1 1 1 1
. 1 1 1 1 1 1
.
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 30 2012
STATUS
approved