A172219 Number of ways to place 4 nonattacking nightriders on a 4 X n board.

1, 16, 84, 412, 1126, 2760, 5739, 10982, 19695, 33068, 52801, 80638, 118731, 169368, 235135, 318890, 423733, 553028, 710389, 899690, 1125059, 1390880, 1701793, 2062694, 2478735, 2955324, 3498125, 4113058, 4806299, 5584280, 6453689

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

Comments

A nightrider is a fairy chess piece that can move (proportionate to how a knight moves) in any direction.

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

Crossrefs

Cf. A061990, A172213, A172218.

Programs

Mathematica

CoefficientList[Series[-(2 x^21 - 6 x^20 + 10 x^19 - 14 x^18 + 22 x^17 - 30 x^16 - 26 x^15 + 162 x^14 - 272 x^13 + 364 x^12 - 466 x^11 + 526 x^10 - 303 x^9 - 207 x^8 + 603 x^7 - 517 x^6 + 489 x^5 - 249 x^4 + 142 x^3 + 14 x^2 + 11 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = (32n^4 - 432n^3 + 3190n^2 - 13323n + 25530)/3, n>=18.

G.f.: -x * (2*x^21 -6*x^20 +10*x^19 -14*x^18 +22*x^17 -30*x^16 -26*x^15 +162*x^14 -272*x^13 +364*x^12 -466*x^11 +526*x^10 -303*x^9 -207*x^8 +603*x^7 -517*x^6 +489*x^5 -249*x^4 +142*x^3 +14*x^2 +11*x +1) / (x-1)^5. - Vaclav Kotesovec, Mar 25 2010