OFFSET
1,2
COMMENTS
The Grasshopper moves on the same lines as a queen, but must jump over a hurdle to land on the square immediately beyond.
REFERENCES
Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p.829
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
Explicit formula (C. Poisson, 1990): a(n) = 1/6*(n-1)(n^5 +n^4 -2*n^3 -22*n^2 +76*n -72).
G.f.: -4*x^2*(3*x^5 -7*x^4 +4*x^3 +17*x^2 +12*x +1)/(x-1)^7.
MATHEMATICA
CoefficientList[Series[-4 x (3 x^5 - 7 x^4 + 4 x^3 + 17 x^2 + 12 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 02 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, May 10 2011
STATUS
approved