A174646 - OEIS

%I #12 Sep 12 2015 11:00:23

%S 0,0,0,0,0,0,0,0,2,100,908,4872,19818,66864,193926,498924,1165544,

%T 2517036,5089430,9731908,17735888,30999920,52234274,85210284,

%U 135059570,208627984,314889330,465423908,674966914,962031720,1349613074

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

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

%H Vincenzo Librandi, <a href="/A174646/b174646.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="http://oprisch.net/SuperQueens/SuperQueens.html">The Oprisch Family Web Site</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>

%F 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.

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

%t 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 *)

%Y Cf. A174642, A174644, A174645.

%K nonn,easy

%O 1,9

%A _Vaclav Kotesovec_, Mar 25 2010