A292882 Number of n-step closed paths on the E7 lattice.

1, 0, 126, 4032, 228690, 14394240, 1020623940, 78353170560, 6393827197170

Offset: 0

Author

Samuel Savitz, Sep 26 2017

Keywords

• nonn
• walk
• more

Comments

Calculated by brute force computational enumeration.

The moments of the imaginary part of the suitably normalized E7 lattice Green's function.

Examples

			The 2-step walks consist of hopping to one of the 126 minimal vectors of the E7 lattice and then back to the origin.
		

Links

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

Crossrefs

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).

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 E7 lattice Green's function.