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A172129 Number of ways to place 5 nonattacking bishops on an n X n board. 13
0, 0, 0, 112, 3368, 39680, 282248, 1444928, 5865552, 20014112, 59673360, 159698416, 391202680, 890095584, 1902427800, 3853570560, 7450556064, 13829016768, 24759442464, 42930138864, 72328779720, 118747638592 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For any fixed value of k>1, a(n) = n^(2k) /k! - 2n^(2k - 1) /3/(k - 2)! + ...

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

FORMULA

Explicit formula: a(n) = n(n - 2)(3n^8 - 34n^7 + 177n^6 - 590n^5 + 1435n^4 - 2592n^3 + 3326n^2 - 2844n + 1344)/360 if n is even; a(n) = (n - 1)(n - 2)(n - 3)(3n^7 - 22n^6 + 80n^5 - 204n^4 + 379n^3 - 464n^2 + 378n - 270)/360 if n is odd.

G.f.: -8x^4*(15x^11+186x^10+1593x^9+6666x^8+17522x^7+28808x^6+31334x^5+22040x^4+9871x^3+2574x^2+337x+14)/((x-1)^11*(x+1)^5). [Vaclav Kotesovec, Mar 25 2010]

MATHEMATICA

CoefficientList[Series[-8 x^3 (15 x^11 + 186 x^10 + 1593 x^9 + 6666 x^8 + 17522 x^7 + 28808 x^6 + 31334 x^5 + 22040 x^4 + 9871 x^3 + 2574 x^2 + 337 x + 14) / ((x-1)^11 (x+1)^5), {x, 0, 50}], x]] (* Vincenzo Librandi, May 02 2013 *)

CROSSREFS

Cf. A108792, A172123, A172124, A172127.

Sequence in context: A267327 A008361 A271671 * A304552 A103860 A265660

Adjacent sequences:  A172126 A172127 A172128 * A172130 A172131 A172132

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 26 2010

STATUS

approved

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Last modified December 18 21:01 EST 2018. Contains 318245 sequences. (Running on oeis4.)