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A173436 Number of ways to place 7 nonattacking knights on an n X n toroidal board. 1
0, 0, 0, 16, 0, 80352, 1359288, 31404480, 339256836, 2527519400, 14053530964, 63100177488, 240356217660, 803630856504, 2416671974700, 6655251717376, 17015566051020, 40822003107000, 92679987456312, 200490192134800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

FORMULA

Explicit formula: a(n) = n^2*(n^12-189n^10+16135n^8-801255n^6+24595984n^4-445931556n^2+3756080880)/5040, n>=14. For any fixed value of k > 1, a(n) = n^(2k)/k! - 9n^(2k-2)/2/(k-2)! + (243k+143)*n^(2k-4)/24/(k-3)! - ...

G.f.: -4*x^4 * (2535*x^24 -61497*x^23 +627330*x^22 -3849410*x^21 +16791330*x^20 -58053150*x^19 +170691269*x^18 -438580125*x^17 +976505385*x^16 -1844050487*x^15 +2900976825*x^14 -3760563305*x^13 +3991133690*x^12 -3450574470*x^11 +2418714751*x^10 -1370750375*x^9 +628081926*x^8 -228075638*x^7 +56855445*x^6 -6423333*x^5 +4868490*x^4 +36682*x^3 +20508*x^2 -60*x +4) / (x-1)^15. [Vaclav Kotesovec, Mar 25 2010]

MATHEMATICA

CoefficientList[Series[- 4 x^3 (2535 x^24 - 61497 x^23 + 627330 x^22 - 3849410 x^21 + 16791330 x^20 - 58053150 x^19 + 170691269 x^18 - 438580125 x^17 + 976505385 x^16 - 1844050487 x^15 + 2900976825 x^14 - 3760563305 x^13 + 3991133690 x^12 - 3450574470 x^11 + 2418714751 x^10 - 1370750375 x^9 + 628081926 x^8 - 228075638 x^7 + 56855445 x^6 - 6423333 x^5 + 4868490 x^4 + 36682 x^3 + 20508 x^2 - 60 x + 4) / (x - 1)^15, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)

CROSSREFS

Cf. A172529, A172530, A172531, A172532, A172533.

Sequence in context: A221759 A111979 A309984 * A081263 A265491 A209201

Adjacent sequences:  A173433 A173434 A173435 * A173437 A173438 A173439

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Feb 18 2010

STATUS

approved

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Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)