|
|
A167981
|
|
Number of 2n-cycles on the graph of the tesseract, 2 <= n <= 8.
|
|
4
|
|
|
|
OFFSET
|
2,1
|
|
COMMENTS
|
The graph of any n-cube (n>1) contains only even length cycles.
The tesseract is the 4 dimensional cube, and is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol for the tesseract is {4,3,3}.
|
|
LINKS
|
|
|
EXAMPLE
|
a(2) = 24 because there are 24 4-cycles on the graph of the tesseract.
The cycle polynomial is 24*x^4 + 128*x^6 + 696*x^8 + 2112*x^10 + 5024*x^12 + 5376*x^14 + 1344*x^16.
|
|
CROSSREFS
|
Cf. A167982 (n-cycles on graph of 16-cell).
Cf. A167983 (n-cycles on graph of 24-cell).
Cf. A167984 (n-cycles on graph of 120-cell).
Cf. A167985 (n-cycles on graph of 600-cell).
Cf. A085452 (2k-cycles on graph of n-cube).
Cf. A144151 (ignoring first three columns (0<=k<=2), k-cycles on (n-1)-simplex).
Cf. A167986 (k-cycles on graph of n-orthoplex).
|
|
KEYWORD
|
fini,full,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|