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

1,7

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) = 1/3*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).

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 *)

Crossrefs

Cf. A172201, A172518, A178972.

Sequence in context: A186395 A230716 A211852 * A259248 A238519 A185884

Adjacent sequences: A178970 A178971 A178972 * A178974 A178975 A178976

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 02 2011

Status

approved