A292883 Number of n-step closed paths on the E8 lattice.

1, 0, 240, 13440, 1260720, 137813760, 17141798400, 2336327078400, 341350907713200

Offset

0,3

Comments

Calculated by brute force computational enumeration.

The moments of the imaginary part of the suitably normalized E8 lattice Green's function.

Links

Table of n, a(n) for n=0..8.

S. Savitz and M. Bintz, Exceptional Lattice Green's Functions, arXiv:1710.10260 [math-ph], 2017.

Formula

Summed combinatorial expressions and recurrence relations for this sequence exist, but have not been determined. These would allow one to write a differential equation or hypergeometric expression for the E8 lattice Green's function.

Example

The 2-step walks consist of hopping to one of the 240 minimal vectors of the E8 lattice and then back to the origin.

Crossrefs

Cf. A126869 (Linear A1 lattice), A002898 (Hexagonal A2), A002899 (FCC A3), A271432 (D4), A271650 (D5), A292881 (E6), A271651 (D6), A292882 (E7), A271670 (D7), A271671 (D8).

Sequence in context: A268902 A232994 A023906 * A292075 A035841 A232428

Adjacent sequences: A292880 A292881 A292882 * A292884 A292885 A292886

Keyword

nonn,walk,more

Author

Samuel Savitz, Sep 26 2017

Status

approved