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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

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

G.f.: -2x^5 * (465x^12 -4432x^11 +14622x^10 -20892x^9 +36103x^8 -162056x^7 +376992x^6 -263140x^5 -287097x^4 +373248x^3 +243562x^2 +24776x +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 * A108904 A091080 A157515

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 August 21 01:18 EDT 2017. Contains 290855 sequences.