A212269 Number of ways to place k non-attacking kings on an n X n cylindrical chessboard, summed over all k >= 0.

2, 5, 19, 205, 3011, 92875, 4763459, 459630701, 78223965193, 24270274906085, 13497818986883771, 13571363009654254429, 24562890586806439035377, 80199120146273882569630015, 471874707649862024071657639861, 5005895207027974222377733802848093

Offset: 1

Author

Vaclav Kotesovec, May 12 2012

Keywords

• nonn
• hard

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 343.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..27
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p.165

Crossrefs

Cf. A063443 (n+1), A067958, A194650-A194654, A182407, A247413, A212269.

Formula

Limit n ->infinity (a(n))^(1/n^2) = 1.342643951124... (see A247413).