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A292881
Number of n-step closed paths on the E6 lattice.
2
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
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
KEYWORD
nonn,walk,more
AUTHOR
Samuel Savitz, Sep 26 2017
STATUS
approved