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 A085452 Triangle T(n,k) read by rows: T(n,k) = number of cycles of length 2k in the binary n-cube, for n >= 2, k = 2, 3, ..., 2^(n-1). 8
 1, 6, 16, 6, 24, 128, 696, 2112, 5024, 5376, 1344, 80, 640, 6720, 68736, 591200, 4652160, 32146800, 185285120, 865894848, 3136412160, 8315531200, 14800412160, 15448366080, 7413471744, 906545760, 240, 2560, 39840, 698112, 12226560, 203258880, 3257746560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Row n contains 2^(n-1)-1 terms. Also the triangle of even-order coefficients (odd coefficients are all 0) of the hypercube graph cycle polynomials ordered from smallest to largest exponent starting with x^4. - Eric W. Weisstein, Feb 05 2014 REFERENCES Initial terms computed by Daniele Degiorgi (danieled(AT)inf.ethz.ch). LINKS Table of n, a(n) for n=2..34. Eric Weisstein's World of Mathematics, Cycle Polynomial Eric Weisstein's World of Mathematics, Hypercube Graph EXAMPLE Triangle begins: 1, 6, 16, 6, 24, 128, 696, 2112, 5024, 5376, 1344, 80, 640, 6720, 68736, 591200, 4652160, 32146800, 185285120, 865894848, 3136412160, 8315531200, 14800412160, 15448366080, 7413471744, 906545760, .... In terms of cycle polynomials: x^4 6*x^4 + 16*x^6 + 6*x^8 24*x^4 + 128*x^6 + 696*x^8 + 2112*x^10 + 5024*x^12 + 5376*x^14 + 1344*x^16 ... MATHEMATICA Table[Table[Length[FindCycle[HypercubeGraph[n], {k}, All]], {k, 4, 2^n, 2}], {n, 4}] // Flatten (* Eric W. Weisstein, Mar 23 2020 *) CROSSREFS Cf. A066037, A001788. Row sums give A085408. Sequence in context: A107777 A136140 A155834 * A028286 A046629 A291795 Adjacent sequences: A085449 A085450 A085451 * A085453 A085454 A085455 KEYWORD nonn,tabf,more,hard AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 12 2003 EXTENSIONS Corrected by Andrew Weimholt, Nov 14 2009 Initial terms of T(6,k) from Eric W. Weisstein, Mar 23 2020 STATUS approved

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Last modified September 8 17:50 EDT 2024. Contains 375753 sequences. (Running on oeis4.)