This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A167983 Number of n-cycles on the graph of the regular 24-cell, 3 <= n <= 24. 4


%S 96,360,1440,7120,37728,196488,974592,4536000,19934208,82689264,

%T 322437312,1171745280,3924079104,11964375936,32761139328,79244294016,

%U 165800420352,291640320576,413774810112,443415854592,318534709248,114869295744

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

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

%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP scripts for various math problems</a>

%H Max A. Alekseyev, GĂ©rard P. Michon, <a href="http://arxiv.org/abs/1602.01396">Making Walks Count: From Silent Circles to Hamiltonian Cycles</a>, arXiv:1602.01396 [math.CO], 2016.

%H A. Weimholt, <a href="http://www.weimholt.com/andrew/24.html">24-cell net</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/24-Cell.html">24-Cell </a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclePolynomial.html">Cycle Polynomial</a>

%e a(3) = 96, because there are 96 3-cycles on the graph of the 24-cell.

%e 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.

%Y Cf. A167981 - 2n-cycles on graph of the tesseract.

%Y Cf. A167982 - n-cycles on graph of 16-cell.

%Y Cf. A167984 - n-cycles on graph of 120-cell.

%Y Cf. A167985 - n-cycles on graph of 600-cell.

%Y Cf. A085452 - T(n, k) = 2k-cycles on graph of n-cube.

%Y Cf. A144151 - ignoring first three columns (0<=k<=2), T(n, k) gives k-cycles on (n-1)-simplex.

%Y Cf. A167986 - T(n, k) = k-cycles on graph of n-orthoplex.

%K fini,full,nonn

%O 3,1

%A _Andrew Weimholt_, Nov 16 2009

%E a(16)-a(24) and "full" keyword from _Max Alekseyev_, Nov 18 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 9 17:46 EST 2016. Contains 278985 sequences.