A137432 Number of ways to place n^2 nonattacking kings on a 2n X 2n cylindrical chessboard.
1, 4, 32, 344, 4460, 66532, 1118398, 20984924, 437500380, 10105541204, 257860425672, 7241521734020, 222770819826574, 7466859257161488, 271156951835070930, 10609740515840572076, 444982726973034212924, 19911203110764903275188, 946564783226311159219150
Offset: 0
Links
- Rintaro Matsuo, Table of n, a(n) for n = 0..384 (terms 1..31 from Alex V. Breger)
- Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, pp. 209-210.
- Artem M. Karavaev, Zealint blog (in Russian)
- Rintaro Matsuo, Polynomial-time algorithm
- Rintaro Matsuo, a(1)..a(800)
Formula
Conjecture: limit of a(n+1)/(n*a(n)) as n->infinity is e.
a(n) ~ c * n^n, where c = 2*exp(1)*(exp(1) - 1)^2 / (exp(1) - 2)^2 = 31.1116835720490503682643922791052352237386275089... - Vaclav Kotesovec, Jul 29 2023, updated Mar 18 2024
Extensions
a(11)-a(12) from Vaclav Kotesovec, Sep 08 2011
a(13)-a(27) from Alex V. Breger, Sep 10 2011
a(28)-a(31) from Alex V. Breger, Sep 12 2011
a(0)=1 prepended by Andrew Howroyd, Mar 26 2023