|
|
A036464
|
|
Number of ways to place two nonattacking queens on an n X n board.
|
|
19
|
|
|
0, 0, 8, 44, 140, 340, 700, 1288, 2184, 3480, 5280, 7700, 10868, 14924, 20020, 26320, 34000, 43248, 54264, 67260, 82460, 100100, 120428, 143704, 170200, 200200, 234000, 271908, 314244, 361340, 413540, 471200, 534688, 604384
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math. Monthly, 101 (1994), 629-639.
|
|
FORMULA
|
a(n) = C(n, 3)*(3*n-1).
|
|
MAPLE
|
f:=n->n^4/2 - 5*n^3/3 + 3*n^2/2 - n/3; [seq(f(n), n=1..200)]; # N. J. A. Sloane, Feb 16 2013
|
|
MATHEMATICA
|
f[k_] := 2 k; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 50}] (* A036464 *)
Table[a[n]/4, {n, 2, 50}] (* A000914 *)
CoefficientList[Series[4 x^2 (2 + x) / (1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, May 02 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 8, 44, 140}, 50] (* Harvey P. Dale, Mar 26 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|