A174558 Number of ways to place 8n nonattacking kings on a 16 x 2n chessboard.

2304, 419933, 28432288, 1134127305, 32580145116, 749160010737, 14677177838054, 254977173389319, 4035559337688370, 59315924213143597, 821112680030028632, 10819171744710664383, 136800806311499633208, 1670597119210336446533, 19804685547188544317522, 228865023358344707514899, 2586924156960003793687130, 28681715460054576813151389, 312656761422008821513384848, 3357651442822195404605813501

Offset

1,1

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000

Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013

Vaclav Kotesovec, G.f.

Index entries for linear recurrences with constant coefficients, order 307.

Formula

Asymptotic formula for number of ways to place m x n nonattacking kings on a 2m x 2n chessboard (this case is m=8): f(m,n) ~ k(m)*n*(m+1)^n

First values of k(m):

k(1)=1,

k(2)=17,

k(3)=231,

k(4)=3051.17509,

k(5)=40881.99638,

k(6)=563050.92363,

k(7)=8008508.28858,

k(8)=117833087.45133

k(9)=1794306724.77472

k(10)=28276454469.76459

k(11)=461049875818.05305

k(12)=7775513990776.97046

k(13)=135589372611110.17367

k(14)=2443990803097108.58764

k(15)=45522076785406201.22572

k(16)=875939597341977670.66777

k(17)=17407856624734801679.11613

k(18)=357216046100723515478.42809

k(19)=7567101689641721175327.80272

Crossrefs

Column k=8 of A350819.

Cf. A174155, A174154, A173782, A173783, A061594, A061593, A018807.

Sequence in context: A170785 A259321 A223302 * A338617 A274578 A031774

Adjacent sequences: A174555 A174556 A174557 * A174559 A174560 A174561

Keyword

nonn

Author

Vaclav Kotesovec, Nov 29 2010

Status

approved