cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Samuel Savitz

Samuel Savitz's wiki page.

Samuel Savitz has authored 3 sequences.

A292883 Number of n-step closed paths on the E8 lattice.

Original entry on oeis.org

1, 0, 240, 13440, 1260720, 137813760, 17141798400, 2336327078400, 341350907713200
Offset: 0

Views

Author

Samuel Savitz, Sep 26 2017

Keywords

Comments

Calculated by brute force computational enumeration.
The moments of the imaginary part of the suitably normalized E8 lattice Green's function.

Examples

			The 2-step walks consist of hopping to one of the 240 minimal vectors of the E8 lattice and then back to the origin.

Links

Crossrefs

Cf. A126869 (Linear A1 lattice), A002898 (Hexagonal A2), A002899 (FCC A3), A271432 (D4), A271650 (D5), A292881 (E6), A271651 (D6), A292882 (E7), A271670 (D7), A271671 (D8).

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 E8 lattice Green's function.

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

Original entry on oeis.org

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

Views

Author

Samuel Savitz, Sep 26 2017

Keywords

Comments

Calculated by brute force computational enumeration.
The moments of the imaginary part of the suitably normalized E7 lattice Green's function.

Examples

			The 2-step walks consist of hopping to one of the 126 minimal vectors of the E7 lattice and then back to the origin.

Links

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).

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.

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

Original entry on oeis.org

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

Views

Author

Samuel Savitz, Sep 26 2017

Keywords

Comments

Calculated by brute force computational enumeration.
The moments of the imaginary part of the suitably normalized E6 lattice Green's function.

Examples

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

Links

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).

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.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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