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A172200 Number of ways to place 2 nonattacking amazons (superqueens) on an n X n board 7
0, 0, 0, 20, 92, 260, 580, 1120, 1960, 3192, 4920, 7260, 10340, 14300, 19292, 25480, 33040, 42160, 53040, 65892, 80940, 98420, 118580, 141680, 167992, 197800, 231400, 269100, 311220, 358092, 410060, 467480, 530720, 600160, 676192, 759220, 849660 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

REFERENCES

Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p.829

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

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

Explicit formula (Christian Poisson, 1990): a(n) = (n - 1)(n - 2)(n - 3)(3n + 8)/6.

G.f.: 4*x^4*(2*x-5)/(x-1)^5. [Colin Barker, Jan 09 2013]

MATHEMATICA

CoefficientList[Series[4 x^3 (2 x - 5) / (x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)

PROG

(MAGMA)[(n-1)*(n-2)*(n-3)*(3*n+8)/6: n in [1..50]]; // Vincenzo Librandi, May 27 2013

CROSSREFS

Cf. A051223, A051224, A036464.

Sequence in context: A225892 A211140 A200431 * A177291 A169711 A281391

Adjacent sequences:  A172197 A172198 A172199 * A172201 A172202 A172203

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 29 2010

STATUS

approved

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Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)