A174645 -id:A174645 - cp's OEIS frontend

A174646 Number of ways to place 7 nonattacking amazons (superqueens) on a 7 X n board.

0, 0, 0, 0, 0, 0, 0, 0, 2, 100, 908, 4872, 19818, 66864, 193926, 498924, 1165544, 2517036, 5089430, 9731908, 17735888, 30999920, 52234274, 85210284, 135059570, 208627984, 314889330, 465423908, 674966914, 962031720, 1349613074

Offset: 1

Vaclav Kotesovec, Mar 25 2010

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
The Oprisch Family Web Site
V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Cf. A174642, A174644, A174645.

CoefficientList[Series[2 x^8 (8 x^22 - 4 x^21 - 9 x^20 + 102 x^18 - 138 x^17 + 29 x^16 + 592 x^15 - 1610 x^14 + 2772 x^13 - 3091 x^12 + 3178 x^11 - 2049 x^10 + 1312 x^9 - 625 x^8 + 1438 x^7 - 449 x^6 + 388 x^5 + 403 x^4 + 148 x^3 + 82 x^2 + 42 x + 1) / (x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)

G.f.: 2*x^9 * (8*x^22 - 4*x^21 - 9*x^20 + 102*x^18 - 138*x^17 + 29*x^16 + 592*x^15 - 1610*x^14 + 2772*x^13 - 3091*x^12 + 3178*x^11 - 2049*x^10 + 1312*x^9 - 625*x^8 + 1438*x^7 - 449*x^6 + 388*x^5 + 403*x^4 + 148*x^3 + 82*x^2 + 42*x + 1)/(x-1)^8.

Explicit formula: a(n) = n^7 - 85n^6 + 3329n^5 - 77911n^4 + 1175240n^3 - 11392990n^2 + 65448630n -171006180, n>=24.

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

Original entry on oeis.org

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

Vaclav Kotesovec, May 26 2010

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

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

Cf. A174642, A174644, A174645, A174646.

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 *)

For n >= 31, a(n) = n^8 -110*n^7 +5684*n^6 -180400*n^5 +3845495*n^4 -56292452*n^3 +551196090*n^2 -3289297810*n +9121996624.

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.

cp's OEIS Frontend

A174646 Number of ways to place 7 nonattacking amazons (superqueens) on a 7 X n board.

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