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

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

Offset

0,3

Comments

Calculated by brute force computational enumeration.

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

Example

The 2-step walks consist of hopping to one of the 126 minimal vectors of the E7 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), A271670 (D7), A292883 (E8), A271671 (D8).

Sequence in context: A036403 A286976 A186816 * A140902 A270512 A037963

Adjacent sequences: A292879 A292880 A292881 * A292883 A292884 A292885

Keyword

nonn,walk,more

Author

Samuel Savitz, Sep 26 2017

Status

approved