A178372 Number of ways to place 8 nonattacking amazons (superqueens) on an 8 X n board.

0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 552, 4738, 27110, 119602, 437640, 1376504, 3835578, 9697416, 22605024, 49208658, 101004522, 197024206, 367556982, 659230078, 1141734758, 1916570390, 3128196492, 4978021504, 7741704218, 11790289180

Offset: 1

Author

Vaclav Kotesovec, May 26 2010

Keywords

• nonn
• easy

Comments

An amazon (superqueen) moves like a queen and a knight.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• V. Kotesovec, Non-attacking chess pieces, 6ed, 2013

Crossrefs

Cf. A174642, A174644, A174645, A174646.

Programs

Mathematica

CoefficientList[Series[- 2 x^9 (72 x^29 - 244 x^28 + 40 x^27 + 1379 x^26 - 3400 x^25 + 4619 x^24 - 6525 x^23 + 10407 x^22 - 8879 x^21 - 901 x^20 + 4213 x^19 + 10475 x^18 - 33273 x^17 + 60823 x^16 - 90147 x^15 + 109862 x^14 - 106589 x^13 + 92686 x^12 - 68408 x^11 + 45714 x^10 - 16426 x^9 + 999 x^8 + 9801 x^7 - 1850 x^6 + 2355 x^5 + 1922 x^4 + 826 x^3 + 461 x^2 + 132 x + 16) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

Formula

For n >= 31, a(n) = n^8 -110*n^7 +5684*n^6 -180400*n^5 +3845495*n^4 -56292452*n^3 [phone]*n^2 -3289297810*n [phone].

G.f.: - 2*x^10*(72*x^29 - 244*x^28 + 40*x^27 + 1379*x^26 - 3400*x^25 + 4619*x^24 - 6525*x^23 + 10407*x^22 - 8879*x^21 - 901*x^20 + 4213*x^19 + 10475*x^18 - 33273*x^17 + 60823*x^16 - 90147*x^15 + 109862*x^14 - 106589*x^13 + 92686*x^12 - 68408*x^11 + 45714*x^10 - 16426*x^9 + 999*x^8 + 9801*x^7 - 1850*x^6 + 2355*x^5 + 1922*x^4 + 826*x^3 + 461*x^2 + 132*x + 16)/(x - 1)^9.