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%I #14 Feb 28 2019 03:15:43
%S 32,102,288,640,960,744
%N Number of n-cycles on the graph of the regular 16-cell, 3 <= n <= 8.
%C Row n=3 of the triangle in A167986
%C The 16-cell is the dual polytope of the tesseract, and is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol for the 16-cell is {3,3,4}.
%H A. Weimholt, <a href="http://www.weimholt.com/andrew/16.html">16-cell net</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/16-Cell.html">16-Cell</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclePolynomial.html">Cycle Polynomial</a>
%e a(3) = 32, because there are 32 3-cycles on the graph of the 16-cell.
%e Cycle polynomial is 32*x^3 + 102*x^4 + 288*x^5 + 640*x^6 + 960*x^7 + 744*x^8.
%Y Cf. A167981 (2n-cycles on graph of the tesseract).
%Y Cf. A167983 (n-cycles on graph of 24-cell).
%Y Cf. A167984 (n-cycles on graph of 120-cell).
%Y Cf. A167985 (n-cycles on graph of 600-cell).
%Y Cf. A085452 (2k-cycles on graph of n-cube).
%Y Cf. A144151 (ignoring first three columns (0<=k<=2), k-cycles on (n-1)-simplex).
%Y Cf. A167986 (k-cycles on graph of n-orthoplex).
%K fini,full,nonn
%O 3,1
%A _Andrew Weimholt_, Nov 16 2009
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