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A190397 Number of ways to place 5 nonattacking grasshoppers on a chessboard of size n x n. 3
0, 0, 28, 1668, 29092, 252584, 1441634, 6222996, 22004086, 66972760, 181332416, 446905476, 1019470032, 2179712872, 4410518630, 8510498516, 15756224370, 28128603736, 48622240660, 81660504068, 133643402268, 213660267432 (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

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) = 1/120*(n^10 -10*n^8 -200*n^7 +1175*n^6 -1136*n^5 -740*n^4 -30520*n^3 +159624*n^2 -289024*n +179175 -135*(-1)^n), n>3.

G.f.: 2x^3*(8*x^12 -60*x^11 +75*x^10 +24*x^9 +441*x^8 -1948*x^7 -893*x^6 +4122*x^5 -8491*x^4 -15988*x^3 -6822*x^2 -694*x -14)/((x-1)^11*(x+1)).

MATHEMATICA

CoefficientList[Series[2 x^2 (8 x^12 - 60 x^11 + 75 x^10 + 24 x^9 + 441 x^8 - 1948 x^7 - 893 x^6 + 4122 x^5 - 8491 x^4 - 15988 x^3 - 6822 x^2 - 694 x - 14) / ((x - 1)^11 (x+1)), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 02 2013 *)

CROSSREFS

Cf. A190395, A190396, A108792.

Sequence in context: A335368 A339120 A194190 * A004705 A182400 A333125

Adjacent sequences:  A190394 A190395 A190396 * A190398 A190399 A190400

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, May 10 2011

STATUS

approved

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Last modified June 18 11:56 EDT 2021. Contains 345098 sequences. (Running on oeis4.)