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A190398 Number of ways to place 3 nonattacking grasshoppers on a toroidal chessboard of size n x n. 4
0, 4, 72, 496, 2100, 6708, 17640, 40384, 83376, 158900, 284108, 482160, 783484, 1227156, 1862400, 2750208, 3965080, 5596884, 7752836, 10559600, 14165508, 18742900, 24490584, 31636416, 40440000, 51195508, 64234620, 79929584 (list; graph; refs; listen; history; text; internal format)
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.

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) = 1/6*n^2*(n^4 -3*n^2 -24*n +74), n>3.

G.f.: -4*x^2*(3*x^8 -17*x^7 +37*x^6 -35*x^5 +11*x^4 +19*x^2 +11*x +1)/(x-1)^7.

MATHEMATICA

CoefficientList[Series[- 4 x (3 x^8 - 17 x^7 + 37 x^6 - 35 x^5 + 11 x^4 + 19 x^2 + 11 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 02 2013 *)

CROSSREFS

Cf.: A190395, A172518.

Sequence in context: A095385 A071683 A192826 * A003752 A062018 A192830

Adjacent sequences:  A190395 A190396 A190397 * A190399 A190400 A190401

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, May 10 2011

STATUS

approved

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)