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%I #12 Feb 28 2019 03:15:36
%S 24,128,696,2112,5024,5736,1344
%N Number of 2n-cycles on the graph of the tesseract, 2 <= n <= 8.
%C Row n=4 of the triangle in A085452
%C The graph of any n-cube (n>1) contains only even length cycles.
%C 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}.
%H A. Weimholt, <a href="http://www.weimholt.com/andrew/tesseract.html">Tesseract Foldout</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclePolynomial.html">Cycle Polynomial</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TesseractGraph.html">Tesseract Graph</a>
%e a(2) = 24 because there are 24 4-cycles on the graph of the tesseract.
%e 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.
%Y Cf. A167982 (n-cycles on graph of 16-cell).
%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 2,1
%A _Andrew Weimholt_, Nov 16 2009