A178410 Number of ways to place 8 nonattacking wazirs on an 8 X n board.
0, 2, 4374, 259289, 4255370, 35093344, 189681689, 771464278, 2559099153, 7285273805, 18416621598, 42342480425, 90097012004, 179755977430, 339666241815, 612682858064, 1061605357051, 1776021648675, 2880784715492
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- V. Kotesovec, Non-attacking chess pieces, 6ed, 2013
Programs
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Mathematica
CoefficientList[Series[- x (8 x^13 - 112 x^12 + 870 x^11 - 2812 x^10 + 15019 x^9 + 41114 x^8 + 494109 x^7 + 2357839 x^6 + 5805509 x^5 + 5762254 x^4 + 2079065 x^3 + 219995 x^2 + 4356 x + 2) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)
Formula
a(n) = (1048576*n^8 -17432576*n^7 +136349696*n^6 -658958720*n^5 +2161896569*n^4 -4945969574*n^3 +7719028159*n^2 -7516702410*n +3494080800) / 2520, n >= 7.
G.f.: -x^2 * (8*x^13 -112*x^12 +870*x^11 -2812*x^10 +15019*x^9 +41114*x^8 +494109*x^7 +2357839*x^6 +5805509*x^5 +5762254*x^4 +2079065*x^3 +219995*x^2 +4356*x +2) / (x-1)^9.
Comments