A178973 Number of ways to place 3 nonattacking amazons (superqueens) on an n X n toroidal board.

0, 0, 0, 0, 0, 0, 588, 3328, 9720, 27600, 59048, 124992, 226460, 408464, 666900, 1086464, 1650768, 2505168, 3610000, 5198400, 7191828, 9945232, 13320220, 17835264, 23265000, 30341584, 38718648, 49401408, 61880780, 77504400, 95550308, 117788672, 143225280, 174144464, 209210400, 251325504, 298732228, 355068048, 418062060, 492217600

Offset: 1

Author

Vaclav Kotesovec, Jan 02 2011

Keywords

• nonn
• easy

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

Crossrefs

Cf. A172201, A172518, A178972.

Programs

Mathematica

CoefficientList[Series[- 4 x^6 (36 x^11 - 47 x^10 - 178 x^9 + 228 x^8 + 354 x^7 - 419 x^6 - 356 x^5 + 297 x^4 + 182 x^3 + 178 x^2 + 538 x + 147) / ((x - 1)^7 (x + 1)^5), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

Formula

a(n) = 1/3*n^2*(n^4/2 -6*n^3 +61*n^2/4 +42*n -285/2 +(3*n^2/4 -6*n +21/2)*(-1)^n), n>=7.

G.f.: -4*x^7 * (36*x^11 -47*x^10 -178*x^9 +228*x^8 +354*x^7 -419*x^6 -356*x^5 +297*x^4 +182*x^3 +178*x^2 +538*x +147)/((x-1)^7*(x+1)^5).