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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 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

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