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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
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
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
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