|
| |
|
|
A190396
|
|
Number of ways to place 4 nonattacking grasshoppers on a chessboard of size n x n.
|
|
3
|
|
|
|
0, 1, 78, 1278, 10002, 50191, 189208, 584958, 1563488, 3737987, 8181786, 16669638, 32003238, 58438623, 102234772, 172344406, 281269668, 446107043, 689807558, 1042679982, 1544166426, 2244921423, 3209227248, 4517779918
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
Table of n, a(n) for n=1..24.
V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)
|
|
|
FORMULA
|
Explicit formula (V. Kotesovec, May 7 2011): a(n) = 1/24*(n^8 -6n^6 -80n^5 +431n^4 -552n^3 -666n^2 +2168n -1392), n>2
G.f.: -x^2*(2x^9 -22x^8 +50x^7 +78x^6 -89x^5 -245x^4 +1224x^3 +612x^2 +69x +1)/(x-1)^9
|
|
|
CROSSREFS
|
Cf.: A190395, A061994
Sequence in context: A128951 A027786 A175383 * A160839 A187590 A172217
Adjacent sequences: A190393 A190394 A190395 * A190397 A190398 A190399
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Vaclav Kotesovec, May 10 2011
|
|
|
STATUS
|
approved
|
| |
|
|
