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A137432
Number of ways to place n^2 nonattacking kings on a 2n X 2n cylindrical chessboard.
24
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, 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
Sequence in context: A123309 A186391 A231446 * A177750 A304911 A224993
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