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A172135 Number of ways to place 4 nonattacking knights on an n X n board. 11
0, 1, 18, 412, 4436, 26133, 111066, 376560, 1080942, 2732909, 6253408, 13204356, 26100160, 48819677, 87137934, 149398608, 247349946, 397168485, 620696612, 946921684, 1413726108, 2069939461, 2977725410, 4215337872 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

a(n) = (n^8 - 54n^6 + 144n^5 + 1019n^4 - 5232n^3 - 2022n^2 + 51120n - 77184)/24, n >= 6. (Karl Fabel, 1966)

G.f.: -x^2 * (48*x^12 -312*x^11 +690*x^10 -390*x^9 -1162*x^8 +3606*x^7 -5142*x^6 +3099*x^5 -345*x^4 +1292*x^3 +286*x^2 +9*x +1) / (x-1)^9. [Vaclav Kotesovec, Mar 25 2010]

MATHEMATICA

CoefficientList[Series[-x (48 x^12 - 312 x^11 + 690 x^10 - 390 x^9 - 1162 x^8 + 3606 x^7 - 5142 x^6 + 3099 x^5 - 345 x^4 + 1292 x^3 + 286 x^2 + 9 x + 1) / (x - 1)^9, {x, 0, 40}], x] (* Vincenzo Librandi, May 26 2013 *)

CROSSREFS

Cf. A061994, A172127, A172132, A172134.

Column k=4 of A244081.

Sequence in context: A260655 A318598 A215229 * A005477 A197343 A289941

Adjacent sequences:  A172132 A172133 A172134 * A172136 A172137 A172138

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 26 2010

STATUS

approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)