A172228 Number of ways to place 5 nonattacking wazirs on an n X n board.

0, 0, 1, 304, 10741, 127960, 870589, 4197456, 16005187, 51439096, 145085447, 369074128, 863338777, 1883786680, 3875953561, 7583888944, 14206566327, 25617069208, 44663199283, 75572017136, 124485188701, 200156902936, 314851577749, 485484612496, 735056106571, 1094434774968

Offset

1,4

Comments

Wazir is a (fairy chess) leaper [0,1].

Links

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

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

Eric Weisstein's World of Mathematics, Grid Graph

Wikipedia, Fairy chess piece

Wikipedia, Wazir (chess)

Formula

a(n) = (n^10-50n^8+40n^7+995n^6-1560n^5-8890n^4+21080n^3+24264n^2-97440n+59520)/120, n>=4.

For any fixed value of k > 1, a(n) = n^(2k)/k! - 5/2/(k-2)!*n^(2k-2) + ...

G.f.: x^3 * (6*x^11 -26*x^10 -93*x^9 +527*x^8 +490*x^7 -6710*x^6 +13630*x^5 -3954*x^4 -26364*x^3 -7452*x^2 -293*x -1) / (x-1)^11. - Vaclav Kotesovec, Apr 29 2011

a(n) = A232833(n,5). - R. J. Mathar, Apr 11 2024

Mathematica

CoefficientList[Series[x^2 (6 x^11 - 26 x^10 - 93 x^9 + 527 x^8 + 490 x^7 - 6710 x^6 + 13630 x^5 - 3954 x^4 - 26364 x^3 - 7452 x^2 - 293 x - 1) / (x - 1)^11, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Crossrefs

Cf. A172225, A172226, A172227, A108792, A061998, A172129, A172136, A172140, A006506.

Sequence in context: A300965 A300922 A301530 * A281329 A293092 A221117

Adjacent sequences: A172225 A172226 A172227 * A172229 A172230 A172231

Keyword

nonn,easy,changed

Author

Vaclav Kotesovec, Jan 29 2010

Extensions

Corrected a(4) and g.f., Vaclav Kotesovec, Apr 29 2011.

More terms from Vincenzo Librandi, May 28 2013

Status

approved