A167981 Number of 2n-cycles on the graph of the tesseract, 2 <= n <= 8.

24, 128, 696, 2112, 5024, 5736, 1344

Offset

2,1

Comments

Row n=4 of the triangle in A085452

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

Table of n, a(n) for n=2..8.

A. Weimholt, Tesseract Foldout

Eric Weisstein's World of Mathematics, Cycle Polynomial

Eric Weisstein's World of Mathematics, Tesseract Graph

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).

Sequence in context: A326367 A182186 A188304 * A185490 A293365 A093699

Adjacent sequences: A167978 A167979 A167980 * A167982 A167983 A167984

Keyword

fini,full,nonn

Author

Andrew Weimholt, Nov 16 2009

Status

approved