An explicit solution to the chessboard pebbling problem

Abstract

We consider the chessboard pebbling problem analysed by Chung et al. [Pebbling a chessboard, Am. Math. Mon. 102 (1995), pp. 113–123]. We study the number of reachable configurations and a related double sequence . The analysis involves solving a difference equation satisfied by . Exact expressions for these are derived, and we then consider various asymptotic limits.

Keywords:

• chessboard pebbling
• reachable configurations
• asymptotics
• difference equation

Acknowledgements

Knessl was partly supported by NSA grants H 98230-08-1-0102 and H 98230-11-1-0184.

Notes

1. [email protected]

Additional information

Notes on contributors

Charles Knessl

1