A292883 - OEIS

%I #12 Oct 31 2017 12:37:37

%S 1,0,240,13440,1260720,137813760,17141798400,2336327078400,

%T 341350907713200

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

%C Calculated by brute force computational enumeration.

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

%H S. Savitz and M. Bintz, <a href="https://arxiv.org/abs/1710.10260">Exceptional Lattice Green's Functions</a>, arXiv:1710.10260 [math-ph], 2017.

%F 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.

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

%Y 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).

%K nonn,walk,more

%O 0,3

%A _Samuel Savitz_, Sep 26 2017