A292881 Number of n-step closed paths on the E6 lattice.

1, 0, 72, 1440, 54216, 2134080, 93993120, 4423628160, 219463602120, 11341793393280

Offset

0,3

Comments

Calculated by brute force computational enumeration.

The moments of the imaginary part of the suitably normalized E6 lattice Green's function.

Links

Table of n, a(n) for n=0..9.

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 E6 lattice Green's function.

Example

The 2-step walks consist of hopping to one of the 72 minimal vectors of the E6 lattice and then back to the origin.

Crossrefs

Cf. A126869 (Linear A1 lattice), A002898 (Hexagonal A2), A002899 (FCC A3), A271432 (D4), A271650 (D5), A271651 (D6), A292882 (E7), A271670 (D7), A292883 (E8), A271671 (D8).

Sequence in context: A128800 A367781 A008391 * A282018 A037251 A352994

Adjacent sequences: A292878 A292879 A292880 * A292882 A292883 A292884

Keyword

nonn,walk,more

Author

Samuel Savitz, Sep 26 2017

Status

approved