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
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 02 2011
STATUS
approved