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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
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
FORMULA
Explicit formula (Christian Poisson, 1990): a(n) = (n - 1)(n - 2)(n - 3)(3n + 8)/6.
G.f.: 4*x^4*(5-2*x)/(1-x)^5. - Colin Barker, Jan 09 2013
E.g.f.: 8 + (1/6)*(-48 +48*x -24*x^2 +8*x^3 +3*x^4)*exp(x). - G. C. Greubel, Apr 28 2022
MATHEMATICA
CoefficientList[Series[4x^3(5-2x)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 0, 20, 92}, 40] (* or *) Table[(n-1)(n-2)(n-3)(3n+8)/6, {n, 40}] (* Harvey P. Dale, May 16 2021 *)
PROG
(Magma) [(n-1)*(n-2)*(n-3)*(3*n+8)/6: n in [1..50]]; // Vincenzo Librandi, May 27 2013
(SageMath) [binomial(n-1, 3)*(3*n+8) for n in (1..50)] # G. C. Greubel, Apr 28 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 29 2010
STATUS
approved