

A190396


Number of ways to place 4 nonattacking grasshoppers on a chessboard of size n x n.


4



0, 1, 78, 1278, 10002, 50191, 189208, 584958, 1563488, 3737987, 8181786, 16669638, 32003238, 58438623, 102234772, 172344406, 281269668, 446107043, 689807558, 1042679982, 1544166426, 2244921423, 3209227248, 4517779918
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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 nonattacking 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)/(x1)^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

Cf.: A190395, A061994.
Sequence in context: A128951 A027786 A175383 * A230521 A264362 A160839
Adjacent sequences: A190393 A190394 A190395 * A190397 A190398 A190399


KEYWORD

nonn,easy


AUTHOR

Vaclav Kotesovec, May 10 2011


STATUS

approved



