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).

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

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