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A172201 Number of ways to place 3 nonattacking amazons (superqueens) on an n X n board. 5
0, 0, 0, 0, 48, 424, 1976, 6616, 17852, 41544, 86660, 166288, 298616, 508200, 827168, 1296744, 1968676, 2907016, 4189772, 5910944, 8182400, 11136168, 14926536, 19732600, 25760588, 33246664, 42459476, 53703216, 67320392, 83695144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

An amazon (superqueen) moves like a queen and a knight.

REFERENCES

Panos Louridas, idee & form 93/2007, pp. 2936-2938.

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 (Panos Louridas, 2007): a(n) = (2n^6 - 20n^5 + 31n^4 + 314n^3 - 1452n^2 + 2040n - 672)/12 if n is even (n >= 4) and a(n) = (2n^6 - 20n^5 + 31n^4 + 314n^3 - 1452n^2 + 2034n - 669)/12 if n is odd (n >= 5).

G.f.: 4x^5*(x^7-7x^6+13x^5+23x^4-32x^3-60x^2-46x-12)/((x+1)^2*(x-1)^7). [Vaclav Kotesovec, Mar 24 2010]

MATHEMATICA

CoefficientList[Series[4 x^4 (x^7 - 7 x^6 + 13 x^5 + 23 x^4 - 32 x^3 - 60 x^2 - 46 x - 12) / ((x + 1)^2 (x - 1)^7), {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)

CROSSREFS

Cf. A051223, A051224, A047659, A061989, A172200.

Sequence in context: A160335 A019558 A232917 * A249293 A281374 A190416

Adjacent sequences:  A172198 A172199 A172200 * A172202 A172203 A172204

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 29 2010

STATUS

approved

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