A167984 Number of n-cycles on the graph of the regular 120-cell, 3 <= n <= 600.

0, 0, 720, 0, 0, 3600, 2400, 4320, 28800, 35400, 64800, 284400, 540000, 1139400, 3708000, 8557200, 19677600, 55725120, 140359200, 346456800, 935942400, 2442469200, 6282571680

Offset

3,3

Comments

The 120-cell is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol of the 120-cell is {5,3,3}.

Links

Table of n, a(n) for n=3..25.

A. Weimholt, 120-cell net

Eric Weisstein's World of Mathematics, 120-Cell

Eric Weisstein's World of Mathematics, Cycle Polynomial

Example

a(5) = 720, because there are 720 5-cycles on the graph of the 120-cell.
Cycle polynomial is 720*x^5 + 3600*x^8 + 2400*x^9 + 4320*x^10 + 28800*x^11 + 35400*x^12 + 64800*x^13 +  284400*x^14 + 540000*x^15 + 1139400*x^16 + 3708000*x^17 + 8557200*x^18 + 19677600*x^19 + 55725120*x^20 + 140359200*x^21 + 346456800*x^22 + 935942400*x^23 + ...

Crossrefs

Cf. A167981 (2n-cycles on graph of the tesseract).

Cf. A167982 (n-cycles on graph of 16-cell).

Cf. A167983 (n-cycles on graph of 24-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).

Cf. A108997 (number of vertices n-steps from a given vertex on graph of 120-cell).

Sequence in context: A139195 A269124 A267336 * A267429 A317660 A267571

Adjacent sequences: A167981 A167982 A167983 * A167985 A167986 A167987

Keyword

fini,more,nonn,hard

Author

Andrew Weimholt, Nov 16 2009

Extensions

a(24) from Eric W. Weisstein, Feb 21 2014

a(25) from Eric W. Weisstein, Mar 11 2014

Status

approved