A172449 Number of ways to place 8 nonattacking queens on an 8 X n board.
0, 0, 0, 0, 0, 0, 0, 92, 1066, 7828, 44148, 195270, 707698, 2211868, 6120136, 15324708, 35312064, 75937606, 153942964, 296590536, 546621416, 968910732, 1659114170, 2754780934, 4449361442, 7009572728, 10796663102, 16292133888
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes
Programs
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Mathematica
CoefficientList[Series[x^7 (-72 x^31 + 360 x^30 - 360 x^29 - 1320 x^28 + 4208 x^27 - 9064 x^26 + 28358 x^25 - 65290 x^24 + 80160 x^23 - 41550 x^22 - 19482 x^21 + 62314 x^20 - 43912 x^19 - 81620 x^18 + 228424 x^17 - 261720 x^16 + 248114 x^15 - 336290 x^14 + 460564 x^13 - 453438 x^12 + 288474 x^11 - 135252 x^10 + 80270 x^9 - 85476 x^8 + 49676 x^7 - 23614 x^6 - 4768 x^5 - 1794 x^4 - 4344 x^3 - 1546 x^2 - 238 x - 92) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)
Formula
a(n) = n^8 - 84*n^7 + 3378*n^6 - 85078*n^5 + 1467563*n^4 - 17723656*n^3 + 145910074*n^2 - 745654756*n + 1802501048, for n >= 31. - Vaclav Kotesovec, Feb 03 2010
G.f.: x^8*(-72*x^31 + 360*x^30 - 360*x^29 - 1320*x^28 + 4208*x^27 - 9064*x^26 + 28358*x^25 - 65290*x^24 + 80160*x^23 - 41550*x^22 - 19482*x^21 + 62314*x^20 - 43912*x^19 - 81620*x^18 + 228424*x^17 - 261720*x^16 + 248114*x^15 - 336290*x^14 + 460564*x^13 - 453438*x^12 + 288474*x^11 - 135252*x^10 + 80270*x^9 - 85476*x^8 + 49676*x^7 - 23614*x^6 - 4768*x^5 - 1794*x^4 - 4344*x^3 - 1546*x^2 - 238*x - 92)/(x-1)^9. - Vaclav Kotesovec, Mar 20 2010