A167983 Number of n-cycles on the graph of the regular 24-cell, 3 <= n <= 24.

96, 360, 1440, 7120, 37728, 196488, 974592, 4536000, 19934208, 82689264, 322437312, 1171745280, 3924079104, 11964375936, 32761139328, 79244294016, 165800420352, 291640320576, 413774810112, 443415854592, 318534709248, 114869295744

Offset

3,1

Comments

The 24-cell is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol of the 24-cell is {3,4,3}.

Links

Table of n, a(n) for n=3..24.

Max Alekseyev, PARI/GP scripts for various math problems

Max A. Alekseyev, Gérard P. Michon, Making Walks Count: From Silent Circles to Hamiltonian Cycles, arXiv:1602.01396 [math.CO], 2016.

A. Weimholt, 24-cell net

Eric Weisstein's World of Mathematics, 24-Cell

Eric Weisstein's World of Mathematics, Cycle Polynomial

Example

a(3) = 96, because there are 96 3-cycles on the graph of the 24-cell.
Cycle polynomial is 96*x^3 + 360*x^4 + 1440*x^5 + 7120*x^6 + 37728*x^7 + 196488*x^8 + 974592*x^9 + 4536000*x^10 + 19934208*x^11 + 82689264*x^12 + 322437312*x^13 + 1171745280*x^14 + 3924079104*x^15 + 11964375936*x^16 + 32761139328*x^17 + 79244294016*x^18 + 165800420352*x^19 + 291640320576*x^20 + 413774810112*x^21 + 443415854592*x^22 + 318534709248*x^23 + 114869295744*x^24.

Crossrefs

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

Cf. A167982 (n-cycles on graph of 16-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: A220540 A292345 A084048 * A248457 A051483 A277107

Adjacent sequences: A167980 A167981 A167982 * A167984 A167985 A167986

Keyword

fini,full,nonn

Author

Andrew Weimholt, Nov 16 2009

Extensions

a(16)-a(24) and "full" keyword from Max Alekseyev, Nov 18 2009

Status

approved