A201369 Number of ways to place 8 nonattacking kings on an n X n board.

0, 0, 0, 0, 27, 21792, 3324193, 119138166, 1979541332, 20142680752, 145977165234, 824771174978, 3850985758339, 15461577137802, 54912339921707, 176153338628674, 518569625849418, 1418340918023792, 3639736652346172, 8833161922947702, 20405252721413369

Offset

1,5

Links

Table of n, a(n) for n=1..21.

V. Kotesovec, Non-attacking chess pieces

Formula

Explicit formula (Vaclav Kotesovec, after values computed by Andrew Woods, Nov 30 2011): (n^16 - 252*n^14 + 336*n^13 + 27762*n^12 - 70896*n^11 - 1699656*n^10 + 6330240*n^9 + 60677169*n^8 - 304864560*n^7 - 1181816748*n^6 + 8314366704*n^5 + 8495481308*n^4 - 121101870624*n^3 + 74007948336*n^2 + 730891869120*n - 1180990460160)/40320, n>=7.

G.f.: -x^5*(14882*x^18 - 180784*x^17 + 1061244*x^16 - 4500406*x^15 + 15038864*x^14 - 34328850*x^13 + 40903004*x^12 - 8667835*x^11 + 23857551*x^10 - 260744627*x^9 + 545801251*x^8 - 276255996*x^7 - 467674682*x^6 + 484515328*x^5 + 391528458*x^4 + 65572237*x^3 + 2957401*x^2 + 21333*x + 27)/(x-1)^17.

Crossrefs

Cf. A061995, A061996, A061997, A061998, A172158, A193580, A194788.

Sequence in context: A167731 A357506 A343692 * A036529 A185882 A278140

Adjacent sequences: A201366 A201367 A201368 * A201370 A201371 A201372

Keyword

nonn

Author

Vaclav Kotesovec, Nov 30 2011

Status

approved