%I #12 Oct 31 2017 12:37:47
%S 1,0,126,4032,228690,14394240,1020623940,78353170560,6393827197170
%N Number of n-step closed paths on the E7 lattice.
%C Calculated by brute force computational enumeration.
%C The moments of the imaginary part of the suitably normalized E7 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 E7 lattice Green's function.
%e The 2-step walks consist of hopping to one of the 126 minimal vectors of the E7 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), A271670 (D7), A292883 (E8), A271671 (D8).
%K nonn,walk,more
%O 0,3
%A _Samuel Savitz_, Sep 26 2017