A172206 Number of ways to place 7 nonattacking kings on a 7 X n board.
0, 0, 24, 926, 37282, 394202, 2484382, 10999618, 38168864, 110899878, 281638602, 643766432, 1352358921, 2651129458, 4906381466, 8648792662, 14623854922, 23851793294, 37697787702, 57953320884, 86929476107, 127563008202, 183536011462, 259410007946, 360775279732
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^2 (3387 x^10 - 13990 x^9 + 57102 x^8 - 55038 x^7 + 217860 x^6 + 137902 x^5 + 324486 x^4 + 120530 x^3 + 30546 x^2 + 734 x + 24) / (x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)
Formula
a(n) = (117649n^7 -2873997n^6 +32197753n^5 -215350695n^4 +932130286n^3 -2618213868n^2 +4424623272n -3468569760)/720, n>=6. For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - 3(k-1)(3k-2)/2/k!*(kn)^(k-1) + ... .
G.f.: x^3*(3387*x^10 -13990*x^9 +57102*x^8 -55038*x^7 +217860*x^6 +137902*x^5 +324486*x^4 +120530*x^3 +30546*x^2 +734*x +24)/(x-1)^8. - Vaclav Kotesovec, Mar 24 2010