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A179424 Number of ways to place 4 nonattacking kings on an n X n toroidal board. 10
0, 0, 0, 12, 575, 9837, 63553, 265008, 853497, 2312925, 5532967, 12037068, 24293243, 46125317, 83243925, 143918272, 239811333, 387002853, 607226187, 929346700, 1391111127, 2041198973, 2941608713, 4170413232, 5824920625, 8025278157, 10918558863, 14683371948, 19535039827, 25731386325 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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: a(n) = 1/24*n^2*(n^6-54*n^4+1019*n^2-6798), n>=5.

G.f.: x^4*(160*x^9 - 963*x^8 + 2054*x^7 - 1308*x^6 - 963*x^5 - 375*x^4 + 5288*x^3 - 5094*x^2 - 467*x - 12)/(x-1)^9.

MATHEMATICA

CoefficientList[Series[x^3 (160 x^9 - 963 x^8 + 2054 x^7 - 1308 x^6 - 963 x^5 - 375 x^4 + 5288 x^3 - 5094 x^2 -467 x - 12) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 01 2013 *)

CROSSREFS

Cf. A061997, A179403, A179404.

Sequence in context: A192604 A192605 A192606 * A316977 A283490 A159722

Adjacent sequences:  A179421 A179422 A179423 * A179425 A179426 A179427

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 07 2011

STATUS

approved

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Last modified April 18 07:59 EDT 2021. Contains 343084 sequences. (Running on oeis4.)