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A178972 Number of ways to place 2 nonattacking amazons (superqueens) on an n X n toroidal board. 4
0, 0, 0, 0, 0, 144, 392, 896, 1620, 2800, 4356, 6624, 9464, 13328, 18000, 24064, 31212, 40176, 50540, 63200, 77616, 94864, 114264, 137088, 162500, 191984, 224532, 261856, 302760, 349200, 399776, 456704, 518364, 587248, 661500, 743904, 832352, 929936, 1034280, 1148800 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
An amazon (superqueen) moves like a queen and a knight.
LINKS
V. Kotesovec, Non-attacking chess pieces, 6ed, 2013
FORMULA
a(n) = 1/2*n^2*(n^2 -4*n -9/2 +(-1)^n/2), n>=5.
G.f.: 4*x^6*(8*x^6 -7*x^5 -30*x^4 +23*x^3 +44*x^2 -26*x -36)/((x-1)^5*(x+1)^3).
MATHEMATICA
CoefficientList[Series[4 x^5 (8 x^6 - 7 x^5 - 30 x^4 + 23 x^3 + 44 x^2 - 26 x - 36) / ((x - 1)^5 (x + 1)^3), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)
CROSSREFS
Sequence in context: A034285 A211469 A248551 * A250787 A188246 A258382
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 02 2011
STATUS
approved

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Last modified June 20 23:53 EDT 2024. Contains 373535 sequences. (Running on oeis4.)