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A172158 Number of ways to place 6 nonattacking kings on an n X n board. 13
0, 0, 0, 0, 978, 62266, 1220298, 12033330, 77784658, 377818258, 1492665418, 5042436754, 15062292834, 40736208186, 101489568538, 235984235970, 517314078210, 1077720399538, 2147500025914, 4114538426818, 7613150953522, 13653752767866, 23808409699242 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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

FORMULA

a(n) = (n^12 - 135*n^10 + 180*n^9 + 7465*n^8 - 18840*n^7 - 202665*n^6 + 751860*n^5 + 2442334*n^4 - 13441200*n^3 - 3643800*n^2 + 89860320*n - 108217440)/720, n>=5. For any fixed value of k > 1, a(n) = n^(2*k)/k! - 9*n^(2*k-2)/2/(k-2)! + 6*n^(2*k-3)/(k-2)! ... -  Vaclav Kotesovec, Jan 27 2010

G.f.: -2*x^5 * (465*x^12 -4432*x^11 +14622*x^10 -20892*x^9 +36103*x^8 -162056*x^7 +376992*x^6 -263140*x^5 -287097*x^4 +373248*x^3 +243562*x^2 +24776*x +489)/(x-1)^13. - Vaclav Kotesovec, Mar 24 2010

MATHEMATICA

CoefficientList[Series[-2 x^4 * (465 x^12 - 4432 x^11 + 14622 x^10 - 20892 x^9 + 36103 x^8 - 162056 x^7 + 376992 x^6 - 263140x^5 -287097 x^4 + 373248 x^3 + 243562 x^2 + 24776 x + 489) / (x - 1)^13, {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)

CROSSREFS

Cf. A061995, A061996, A061997, A061998.

Sequence in context: A077380 A063052 A231708 * A327825 A108904 A091080

Adjacent sequences:  A172155 A172156 A172157 * A172159 A172160 A172161

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 27 2010

EXTENSIONS

More terms from Vincenzo Librandi, May 27 2013

STATUS

approved

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Last modified October 21 23:08 EDT 2020. Contains 337944 sequences. (Running on oeis4.)