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A172134 Number of ways to place 3 nonattacking knights on an n X n board. 13
0, 4, 36, 276, 1360, 4752, 13340, 32084, 68796, 135040, 247152, 427380, 705144, 1118416, 1715220, 2555252, 3711620, 5272704, 7344136, 10050900, 13539552, 17980560, 23570764, 30535956, 39133580, 49655552, 62431200, 77830324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

E. Bonsdorff, K. Fabel, O. Riihimaa, Schach und Zahl, 1966, p. 51-63

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 (Karl Fabel, 1966): a(n) = (n - 2)(n + 5)(n^4 - 3n^3 - 8n^2 + 66n - 108)/6, n >= 4.

G.f.: 4*x^2*(3*x^8-20*x^7+43*x^6-38*x^5+23*x^4-11*x^3-27*x^2-2*x-1)/(x-1)^7. [Vaclav Kotesovec, Mar 25 2010]

MATHEMATICA

CoefficientList[Series[4 x (3 x^8 - 20 x^7 + 43 x^6 - 38 x^5 + 23 x^4 - 11 x^3 - 27 x^2 - 2 x - 1) / (x-1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, May 02 2013 *)

CROSSREFS

Cf. A047659, A172124, A172132.

Column k=3 of A244081.

Sequence in context: A144889 A176097 A173429 * A098916 A316297 A180170

Adjacent sequences:  A172131 A172132 A172133 * A172135 A172136 A172137

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 26 2010

STATUS

approved

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Last modified December 18 21:01 EST 2018. Contains 318245 sequences. (Running on oeis4.)