A201548 Number of ways to place 10 nonattacking wazirs on an n X n toroidal board.

0, 0, 0, 0, 10, 308574, 81442802, 5296005568, 146127335256, 2309813476870, 24738873315596, 198759048859008, 1279605298916568, 6906427308782106, 32277449304595350, 133788325435448576, 500896430870051174, 1718268150463137018, 5462521782760829320, 16243031089247644800

Offset

1,5

Comments

Wazir is a leaper [0,1].

Links

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

V. Kotesovec, Non-attacking chess pieces

Formula

Explicit formula: n^20/3628800 - n^18/16128 + 773*n^16/120960 - 761*n^14/1920 + 2820613*n^12/172800 - 356093*n^10/768 + 412940467*n^8/45360 - 2408161207*n^6/20160 + 24029851729*n^4/25200 - 3541971*n^2, n>=11.

G.f.: 2*x^5*(10*x^26 - 615*x^25 + 14637*x^24 - 193410*x^23 + 1669110*x^22 - 10270682*x^21 + 47718030*x^20 - 174153546*x^19 + 511148331*x^18 - 1213451007*x^17 + 2302816572*x^16 - 3418379599*x^15 + 4006461091*x^14 - 4626995415*x^13 + 8410419611*x^12 - 19068629603*x^11 + 33871890471*x^10 - 39181017568*x^9 + 18018811352*x^8 - 5120263515*x^7 - 178499919965*x^6 - 123414145507*x^5 - 25801931589*x^4 - 1825246983*x^3 - 37482424*x^2 - 154182*x - 5)/(x-1)^21.

Mathematica

CoefficientList[Series[2 x^4 (10 x^26 - 615 x^25 + 14637 x^24 - 193410 x^23 + 1669110 x^22 - 10270682 x^21 + 47718030 x^20 - 174153546 x^19 + 511148331 x^18 - 1213451007 x^17 + 2302816572 x^16 - 3418379599 x^15 + 4006461091 x^14 - 4626995415 x^13 + 8410419611 x^12 - 19068629603 x^11 + 33871890471 x^10 - 39181017568 x^9 + 18018811352 x^8 - 5120263515 x^7 - 178499919965 x^6 - 123414145507 x^5 - 25801931589 x^4 - 1825246983 x^3 - 37482424 x^2-154182 x - 5) / (x - 1)^21, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 04 2013 *)

Crossrefs

Cf. A201236, A201237, A201238, A201239, A201240, A201241, A201242, A201547.

Sequence in context: A080269 A080319 A242854 * A363197 A281361 A177466

Adjacent sequences: A201545 A201546 A201547 * A201549 A201550 A201551

Keyword

nonn,easy

Author

Vaclav Kotesovec, Dec 02 2011

Status

approved