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A178973 Number of ways to place 3 nonattacking amazons (superqueens) on an n X n toroidal board. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,7
COMMENTS
An amazon (superqueen) moves like a queen and a knight.
LINKS
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
Sequence in context: A186395 A230716 A211852 * A259248 A238519 A185884
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 02 2011
STATUS
approved

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Last modified June 23 14:31 EDT 2024. Contains 373651 sequences. (Running on oeis4.)