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

0,2

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

Crossrefs

Cf. A018807, A173033.

Sequence in context: A123309 A186391 A231446 * A177750 A304911 A224993

Adjacent sequences: A137429 A137430 A137431 * A137433 A137434 A137435

Keyword

nonn,nice

Author

Vaclav Kotesovec, Aug 31 2011

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

Status

approved