A178499 Number of ways to place 6 nonattacking knights on an n X n board.

0, 0, 0, 170, 13384, 257318, 2774728, 20202298, 110018552, 481719518, 1781124856, 5756568738, 16676946372, 44127887910, 108192675468, 248568720338, 539925974784, 1116836380926, 2212958151968, 4220919779218

Offset

1,4

Links

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

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013

Formula

Explicit formula: a(n) = n^12/720-(3*n^10)/16+n^9/2+(1553*n^8)/144-(163*n^7)/3-(4493*n^6)/16+(4721*n^5)/2+(578777*n^4)/360-(143156*n^3)/3+(124917*n^2)/2+374990*n-899982, n >= 10.

G.f.: -2*x^4 * (200*x^18 -1540*x^17 +2602*x^16 +15442*x^15 -98586*x^14 +256698*x^13 -336146*x^12 +70977*x^11 +587107*x^10 -1302115*x^9 +1569905*x^8 -1100786*x^7 +367130*x^6 -212358*x^5 +247682*x^4 +212463*x^3 +48293*x^2 +5587*x +85) / (x-1)^13.

Mathematica

CoefficientList[Series[- 2 x^3 (200 x^18 - 1540 x^17 + 2602 x^16 + 15442 x^15 - 98586 x^14 + 256698 x^13 - 336146 x^12 + 70977 x^11 + 587107 x^10 - 1302115 x^9 + 1569905 x^8 - 1100786 x^7 + 367130 x^6 - 212358 x^5 + 247682 x^4 + 212463 x^3 + 48293 x^2 + 5587 x + 85) / (x - 1)^13, {x, 0, 40}], x] (* Vincenzo Librandi, May 31 2013 *)

Crossrefs

Cf. A172132, A172134, A172135, A172136.

Column k=6 of A244081.

Sequence in context: A289648 A187520 A210784 * A133328 A098244 A250957

Adjacent sequences: A178496 A178497 A178498 * A178500 A178501 A178502

Keyword

nonn,easy

Author

Vaclav Kotesovec, May 28 2010

Status

approved