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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 (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

Computed by Daniele Degiorgi (danieled(AT)INF.ETHZ.CH).

LINKS

Table of n, a(n) for n=2..27.

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

...

CROSSREFS

Cf. A066037, A001788. Row sums give A085408.

Sequence in context: A107777 A136140 A155834 * A028286 A046629 A183127

Adjacent sequences:  A085449 A085450 A085451 * A085453 A085454 A085455

KEYWORD

nonn,tabf

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 12 2003

EXTENSIONS

Corrected by Andrew Weimholt, Nov 14 2009

STATUS

approved

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Last modified March 30 04:55 EDT 2017. Contains 284296 sequences.