OFFSET
1,3
COMMENTS
The Grasshopper moves on the same lines as a queen, but must jump over a hurdle to land on the square immediately beyond.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)
FORMULA
a(n) = 1/24*(n^8 -6*n^6 -80*n^5 +431*n^4 -552*n^3 -666*n^2 +2168*n -1392), n>2.
G.f.: -x^2*(2*x^9 -22*x^8 +50*x^7 +78*x^6 -89*x^5 -245*x^4 +1224*x^3 +612*x^2 +69*x +1)/(x-1)^9.
MATHEMATICA
CoefficientList[Series[- x (2 x^9 - 22 x^8 + 50 x^7 + 78 x^6 - 89 x^5 - 245 x^4 + 1224 x^3 + 612 x^2 + 69 x + 1) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 02 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, May 10 2011
STATUS
approved