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A292882 Number of n-step closed paths on the E7 lattice. 2
1, 0, 126, 4032, 228690, 14394240, 1020623940, 78353170560, 6393827197170 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,walk,more
AUTHOR
Samuel Savitz, Sep 26 2017
STATUS
approved

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Last modified July 13 09:39 EDT 2024. Contains 374274 sequences. (Running on oeis4.)