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A300695
Irregular triangle read by rows: T(n, k) = number of vertices with rank k in cocoon concertina n-cube.
2
1, 1, 1, 1, 3, 3, 1, 1, 6, 13, 6, 13, 6, 1
OFFSET
0,5
COMMENTS
Although the cocoon concertina n-cube has no ranks for n>2, its inner vertices can be forced on the rank layers of the convex solid.
Sum of row n is the number of vertices of a cocoon concertina n-cube, i.e., A000696(n).
The rows are palindromic. Their lengths are the central polygonal numbers A000124 = 1, 2, 4, 7, 11, 16, 22, ... That means after row 0 rows of even and odd length follow each other in pairs.
A300699 is a triangle of the same shape that shows the number of ranks in convex concertina hypercubes.
LINKS
Tilman Piesk, ranks 1 / 5, 2 / 4 and 3 for n=3
Tilman Piesk, Python code used to generate the sequence (currently unfinished, does not find all ranks for n>3)
EXAMPLE
First rows of the triangle:
k 0 1 2 3 4 5 6
n
0 1
1 1 1
2 1 3 3 1
3 1 6 13 6 13 6 1
CROSSREFS
KEYWORD
nonn,tabf,more
AUTHOR
Tilman Piesk, Mar 13 2018
STATUS
approved