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A292883
Number of n-step closed paths on the E8 lattice.
2
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
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
KEYWORD
nonn,walk,more
AUTHOR
Samuel Savitz, Sep 26 2017
STATUS
approved