A178972 Number of ways to place 2 nonattacking amazons (superqueens) on an n X n toroidal board.

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

Offset

1,6

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Cf. A172200, A172517.

Sequence in context: A034285 A211469 A248551 * A250787 A188246 A258382

Adjacent sequences: A178969 A178970 A178971 * A178973 A178974 A178975

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 02 2011

Status

approved